Method for generating a reference signal sequence using grouping

ABSTRACT

Method for generating reference signal sequence using grouping is explained. In this method, base sequences are grouped such that each group contains at least one base sequence of each length, so UE(s) can use various length sequences as a reference signal. And in this method, inter cell interference caused by using various length sequence as a reference signal sequence can be minimized by grouping sequences having the high cross correlation relation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 15/445,948, filed on Feb. 28, 2017, now U.S. Pat. No. 9,800,364, which is a continuation of U.S. patent application Ser. No. 14/730,124, filed on Jun. 3, 2015, now U.S. Pat. No. 9,654,244, which is a continuation of U.S. patent application Ser. No. 13/926,855, filed on Jun. 25, 2013, now U.S. Pat. No. 9,077,596, which is a continuation of U.S. patent application Ser. No. 13/341,358, filed on Dec. 30, 2011, now U.S. Pat. No. 8,509,283, which is a continuation of U.S. patent application Ser. No. 13/084,397, filed on Apr. 11, 2011, now U.S. Pat. No. 8,111,732, which is a continuation of U.S. patent application No. 12/024,884, filed Feb. 1, 2008, now U.S. Pat. No. 7,949,033, which claims the benefit of earlier filing date and right of priority to Korean Patent Application Nos. 10-2007-0047494, filed on May 16, 2007, 10-2007-0099707, filed on Oct. 4, 2007, 10-2007-0108226, filed on Oct. 26, 2007 and 10-2007-0109089, filed on Oct. 29, 2007, and also claims the benefit of U.S. Provisional Application Nos. 60/888,065, filed on Feb. 2, 2007, 60/984,386, filed on Nov. 1, 2007 and 61/019,588, filed on Jan. 7, 2008, the contents of which are all hereby incorporated by reference herein in their entirety.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to method for generating a reference signal sequence, and more particularly, to a method for grouping sequences having a variable length corresponding one or multiple of a resource block size, a method for generating a reference signal sequence and a method for generating a reference signal sequence using Zadoff-Chu (ZC) sequence.

Discussion of the Related Art

Following explanation is mainly discussed in view of 3GPP LTE system, but the present invention is not limited to this system, and exemplary 3GPP LTE system is only for making those skilled in the art clearly understand the present invention.

There are a lot of sequences used for transmitting signal, but in 3GPP LTE (3^(rd) Generation Partnership Project Long Term Evolution) system, CAZAC (Constant Amplitude Zero Auto-Correlation) sequence forms the basis sequence for transmitting signals. CAZAC sequence can be used to various channels for extracting ID or control information, such as uplink/downlink synchronization channels (SCH) including P-SCH (primary SCH) and S-SCH (Secondary SCH), pilot channel for transmitting reference signal. And, the CAZAC sequence can be used in scrambling.

Two types of CAZAC sequences, i.e., GCL CAZAC sequence and Zadoff-Chu CAZAC sequence are mainly used as the CAZAC sequences. The two types of CAZAC sequences are associated with each other by a conjugate complex relation. That is, the GCL CAZAC sequence can be acquired by conjugate complex calculation for the Zadoff-Chu CAZAC sequence. The Zadoff-Chu CAZAC sequence is given as follows.

$\begin{matrix} {{c\left( {{k;N},M} \right)} = {{\exp\left( \frac{j\;\pi\;{{Mk}\left( {k + 1} \right)}}{N} \right)}\mspace{14mu}\left( {{for}\mspace{14mu}{odd}\mspace{14mu} N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack \\ {{c\left( {{k;N},M} \right)} = {{\exp\left( \frac{j\;\pi\;{Mk}^{2}}{N} \right)}\mspace{14mu}\left( {{for}\mspace{14mu}{even}\mspace{14mu} N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack \end{matrix}$

where k represents a sequence component index, N represents a length of CAZAC sequence to be generated, and M represents sequence ID or sequence index.

When the Zadoff-Chu CAZAC sequence given by the Equations 1 and 2 and the GCL CAZAC sequence which is a conjugate complex relation with the Zadoff-Chu CAZAC sequence are represented by c(k;N,M), these sequence can have three features as follows.

$\begin{matrix} {{{C\left( {k;N;M} \right)}} = {1\mspace{14mu}\left( {{{for}\mspace{14mu}{all}\mspace{14mu} k},N,M} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack \\ {{R_{M\text{:}N}(d)} = \left\{ \begin{matrix} {1,\left( {{{for}\mspace{14mu} d} = 0} \right)} \\ {0,\left( {{{for}\mspace{20mu} d} \neq \; 0} \right)} \end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack \\ {{R_{{M\; 1},{{M\; 2};N}}(d)} = {p\mspace{14mu}\left( {{{for}\mspace{14mu}{all}\mspace{14mu} M_{1}},{M_{2}\mspace{14mu}{and}{\mspace{11mu}\;}N}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \end{matrix}$

The Equation 3 means that the CAZAC sequence always has a size of 1, and the Equation 4 shows that an auto-correlation function of the CAZAC sequence is expressed by a delta function. In this case, the auto-correlation is based on circular correlation. Also, the Equation 5 shows that a cross-correlation is always a constant.

Among these two kinds of CAZAC sequence, the following explanation is mainly focused on the Zadoff Chu sequence (hereinafter “ZC sequence”).

In the 3GPP LTE system, using this ZC sequence as reference signal sequence, the length of the ZC sequence should be equal to the resource block size. And, not only using one resource block size sequence, but the reference signal sequence having the length corresponding to multiples of resource block size can be used.

For a single-cell environment, the reference signals are transmitted by the localized FDM (Frequency Divisional Multiplexing) method for multiplexing signals from multiple user equipments (UEs). But, for the multi-cell environment, the reference signals are transmitted by the additional CDM (Code Divisional Multiplexing) method for distinguishing the signals from that of the neighboring cells. In this multiplexing, two type of method is possible. One is a CDM method using a ZC sequence having a different root indexes, and the other is a CDM method using a ZC sequence having the same root index (M) and but having differently applied cyclic shift.

When the length of the reference signals using these kinds of ZC sequences is same, the cross correlation values for both of the cases are not large. But, when the reference signals having a difference length came as interference from the neighboring cells and transmitted through the same frequency band or overlapped frequency band, the cross correlation value would be significant.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to provide a method for generating reference signal sequence, which minimizes the interference caused by the signals having different length, came from the neighboring cells.

For this method, the present invention also provides a method for effectively grouping sequences such that each of the group is consisted of the sequences having high cross correlation value, and supports variable length sequences to be used as a reference signals.

Also, the present invention provides a method for generating reference signal sequence based on the above grouping.

To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method for grouping sequences having a variable length corresponding one or multiple of a resource block size is provided. According to one embodiment, the method comprises: grouping the sequences into groups such that each of the groups contains at least one sequence of each length, wherein the grouped sequence is a base sequence which is used for applying a cyclic shift corresponding to variable cyclic shift value, and the base sequence with the cyclic shift is used as a reference signal sequence.

Preferably, a number of the groups is 30.

And, said grouping may be performed such that each of the groups contains one base sequence of each length corresponding to 1 to 5 times of the resource block size, and two base sequences of each length corresponding to 6 or more times of the resource block size.

And, preferably, the base sequence having a length corresponding to 3 or more times of the resource block size is defined by using a Zadoff-Chu (ZC) sequence, and the base sequence having a length corresponding to 1 or 2 times of the resource block size is defined by using other sequence other than the ZC sequence.

In another aspect of the present invention, a method for generating a reference signal sequence is provided. In one embodiment for this aspect, the method comprises: defining one or more base sequences having a variable length corresponding to one or multiple of a resource block size; and applying a cyclic shift corresponding to variable cyclic shift value to the defined base sequence, wherein the base sequences are divided into groups, and each of the group comprises at least one base sequence of each length.

In this case, the base sequence may be defined by cyclic extension of the ZC sequence having a length (N_(zc) ^(RS)) given by a largest prime number which is less than a corresponding reference signal sequence size. Also the base sequence may be defined by truncation of the ZC sequence having a length (N_(zc) ^(RS)) given by the smallest prime number which is larger than a corresponding reference signal sequence size.

Also in this embodiment, preferably, a number of the groups is 30.

And, each of the groups may contain one base sequence of each length corresponding to 1 to 5 times of the resource block size, and two base sequences of each length corresponding to 6 or more times of the resource block size.

And, the base sequence having a length corresponding to 3 or more times of the resource block size may be defined by using a Zadoff-Chu (ZC) sequence with specific ZC sequence index (q), and the base sequence having a length corresponding to 1 or 2 times of the resource block size may be defined by using other sequence other than the ZC sequence.

And, preferably, the specific ZC sequence index (q) is a function of a group index (u) and a base sequence number index (v) within the group.

And, the defined base sequence with cyclic shift may be used for uplink reference signal sequence.

Also for above embodiments, the resource block size may correspond to a size of 12 subcarriers in a frequency domain.

In another aspect of the present invention, a method for generating a reference signal sequence using Zadoff-Chu (ZC) sequence is provided. In on embodiment for this aspect, the method comprises: defining a specific base sequence using q-th root ZC sequence, wherein the base sequences are divided into groups, and the “q” is a function of a group index (u) and a base sequence number index (v) within the group; and applying a cyclic shift corresponding to variable cyclic shift value to the defined base sequence to generate the reference signal sequence.

In one case, the specific ZC sequence index (q) may be determined by one of equations of,

$\begin{matrix} {\mspace{79mu}{{q = {{{round}(y)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}{({{{round}{(y)}} - y})}} + v}}}}{where}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS}}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v\; \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}},}}} & (1) \\ {\mspace{79mu}{{q = {{{round}(y)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}{({{{round}{(y)}} - y})}} + v}}}}{where}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS} - 1}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}},\mspace{14mu}{or}}}} & (2) \\ {\mspace{79mu}{{q = {{{round}(y)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}{({{{round}{(y)}} - y})}} + v}}}}{where}{{y = {{{round}\left( \frac{N_{zc}^{RS}}{N_{{reference},\;{zc}}^{RS}} \right)} \cdot \left( {u + 1} \right)}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\;{v\; \in {\left\{ {0,1,\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}.}}}}} & (3) \end{matrix}$

wherein N_(zc) ^(RS) is the length given by the largest prime number which is less than the corresponding reference signal sequence size, N_(reference,zc) ^(RS) is the corresponding reference signal sequence size, the “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. But, N_(zc) ^(RS) can be the length given by the smallest prime number which is greater than the corresponding reference signal sequence, for another embodiment of this invention.

In the other case, the specific ZC sequence index (q) may be determined by one of equations of,

$\begin{matrix} {\mspace{85mu}{{q = {{{floor}\left( {y + 0.5} \right)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}{({{{round}{({y + 0.5})}} - y})}} + v}}}}{where}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS}}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v\; \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}},}}} & (1) \\ {\mspace{79mu}{{q = {{{floor}\left( {y + 0.5} \right)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}{({{{round}{({y + 0.5})}} - y})}} + v}}}}{where}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS} - 1}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}},\mspace{14mu}{or}}}} & (2) \\ {\mspace{79mu}{{q = {{{floor}\left( {y + 0.5} \right)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}{({{{round}{({y + 0.5})}} - y})}} + v}}}}{where}{{y = {{{floor}\left( {\frac{N_{zc}^{RS}}{N_{{reference},\;{zc}}^{RS}} + 0.5} \right)} \cdot \left( {u + 1} \right)}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\;{v\; \in {\left\{ {0,1,\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}.}}}}} & (3) \end{matrix}$

wherein N_(zc) ^(RS) is the length given by the largest prime number which is less than the corresponding reference signal sequence size, N_(reference,zc) ^(RS) is the corresponding reference signal sequence size, the “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. But, N_(zc) ^(RS) can be the length given by the smallest prime number which is greater than the corresponding reference signal sequence, for another embodiment of this invention.

In one specific embodiment of this invention, the maximum number of the base sequence number index (v) within each group may be set to is 2, and then the specific ZC sequence index (q) can be determined by one of equations of,

$\begin{matrix} {{q = {{{round}(y)} + {v \cdot \left( {- 1} \right)^{{floor}{({2y})}}}}}{where}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS}}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}} & (1) \\ {{q = {{{round}(y)} + {v \cdot \left( {- 1} \right)^{{floor}{({2y})}}}}}{where}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS} - 1}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}\;,\mspace{11mu}{or}}} & (2) \\ {{q = {{{round}(y)} + {v \cdot \left( {- 1} \right)^{{floor}{({2y})}}}}}{where}{{y = {\left( \frac{N_{zc}^{RS}}{N_{{reference},\;{zc}}^{RS}} \right) \cdot \left( {u + 1} \right)}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in {\left\{ {0,1} \right\}.}}}} & (3) \end{matrix}$

rr by one of equations of,

$\begin{matrix} {\mspace{79mu}{{q = {{{floor}\left( {y + 0.5} \right)} + {v \cdot \left( {- 1} \right)^{{floor}{({2y})}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS}}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}}} & (1) \\ {\mspace{79mu}{{q = {{{floor}\left( {y + 0.5} \right)} + {v \cdot \left( {- 1} \right)^{{floor}{({2y})}}}}}\mspace{20mu}{where}\mspace{20mu}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS} - 1}},{u\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}\;,\mspace{11mu}{or}}}} & (2) \\ {\mspace{79mu}{{q = {{{floor}\left( {y + 0.5} \right)} + {v \cdot \left( {- 1} \right)^{{floor}{({2y})}}}}}\mspace{85mu}{where}{{y = {{{{floor}\left( {\frac{N_{zc}^{RS}}{N_{{reference},\;{zc}}^{RS}} + 0.5} \right)} \cdot \left( {u + 1} \right)}\; \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}}},{v \in {\left\{ {0,1} \right\}.}}}}} & (3) \end{matrix}$

Preferably, N_(reference,zc) ^(RS) can be set to 31 or 37, but N_(reference,zc) ^(RS) can be set to other values as well.

According to these embodiments of this invention, because the base sequence for applying cyclic shift is grouped, and each group contains at least one base sequence of each length, UE(s) can use various length sequences as a reference signal sequence when specific group is allocated to one cell or Node B.

Additionally, because each group contains base sequences having high cross correlation relation, if each group is allocated to one cell or Node B, inter cell interference can be minimized.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a further understanding of the invention, illustrate embodiments of the invention and together with the description serve to explain the principle of the invention.

In the drawings:

FIG. 1 shows a conceptual diagram for explaining the truncated sequence generation method.

FIG. 2 shows a conceptual diagram for explaining the generation method using padding part.

FIGS. 3 to 5 show conceptual diagrams of grouping sequences according to one embodiment of this invention.

DETAILED DESCRIPTION OF THE INVENTION

Hereinafter, the preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It is to be understood that the detailed description which will be disclosed along with the accompanying drawings is intended to describe the exemplary embodiments of the present invention, and is not intended to describe a unique embodiment which the present invention can be carried out.

Hereinafter, the detailed description includes detailed matters to provide full understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention can be carried out without the detailed matters. To prevent the concept of the present invention from being ambiguous, structures and apparatuses of the known art will be omitted, or will be shown in the form of a block diagram based on main functions of each structure and apparatus. Also, wherever possible, the same reference numbers will be used throughout the drawings and the specification to refer to the same or like parts.

As stated above, the present invention is directed to provide a method for generating reference signal sequence, which minimizes the interference caused by the signals having different length, came from the neighboring cells.

To this end, the length of the CAZAC sequence is explained.

Presently, in the 3GPP LTE system, the resource block (RB) size for transmitting all kind of the OFDM symbol including reference signal symbol corresponds to the size of 12 subcarriers. So, when ZC is generated for uplink reference signal sequence, the size of ZC sequence would correspond to 12 subcarriers size.

For the case of CAZAC sequence, the number of CAZAC sequence indexes (M) which could be distinguished from each other is decided by the number of relative prime number relative prime to the sequence length (N). So, when the ZC sequence is generated to have the length of 12, the number of ZC sequences having a different sequence index is 4. But, if the ZC sequence is generated based on the prime number length (N), the number of ZC sequence having a different sequence index can be N−1, which maximizes the number of ZC sequence. Therefore, various methods for generating CAZAC sequence based on the prime number length are provided.

First, a truncated sequence generation method is explained.

FIG. 1 shows a conceptual diagram for explaining the truncated sequence generation method.

As shown in the FIG. 1, when the required CAZAC sequence length is “L”, CAZAC sequence having the prime number length of “X” (where X>L) is generated. And, the generated CAZAC sequence having the length “X” is truncated to have the length “L”, that is, part of the sequence having the length of “X−L” is truncated.

By this method, the number of CAZAC sequence is maximized. But because part of the generated sequence is truncated, the auto/cross correlation properties of CAZAC sequence explained with the equations 4 and 5 are somewhat deteriorated. And, when the sequences having poor correlation properties are eliminated, the actual number of sequence is diminished. Moreover, because of the truncation, good PAPR property of CAZAC sequence can also be deteriorated.

So, another type of methods for generating CAZAC sequence based on the prime number is presented. One of these method is that the CAZAC sequence is generated to have the prime number length “X” (where X<L), and components having the length of “L−X” is added to the generated CAZAC sequence. This components added to the generated sequence can be called as padding part, so this method can be called as generation method using padding part.

FIG. 2 shows a conceptual diagram for explaining the generation method using padding part.

As shown in the FIG. 2, when the required CAZAC sequence length is “L”, the CAZAC sequence is generated to have the length “X”, which is a maximum prime number smaller than “L”. And, the padding part having the length of “L-X” is added to the generated sequence.

In one method for this kind of methods, the padding part can be consisted of zeros. By this method, the number of CAZAC sequence can be maximized. Moreover, the auto/cross correlation properties of the CAZAC sequence can be maintained when distinction of the sequences is done with regard to the length of “C1” in FIG. 2.

And, preferably, the padding part can be a cyclic extension of the CAZAC sequence. That is, the padding part (C2) can be generated by cyclic copying of the first part of the generated CAZAC sequence, and be added to the generated sequence. By doing so, the resultant sequence can have a good auto-cross correlation propertied even when the distinction of the sequence is done with regard to the entire sequence length (L). So, this method has further advantage than the above method using the padding part as zeros.

The present invention for generating reference signal sequence using CAZAC sequence is mainly based on the generation method using padding part generated by the above mentioned cyclic extension. But, limitation to this generation method is not necessary, that is, present invention can be based on the truncated sequence generation method and the generation method using padding part consisted of zeros.

Based on this, the inter cell interference caused by using sequences having difference length is explained.

When CAZAC sequence is used for reference signal sequence, the inter cell interference is proportional to the cross correlation value between two sequence. So, in the following examples, the cross correlation value, caused by the overlapping between the original reference signal transmitted through certain resource region and the incoming sequence came from the neighboring cells, having difference length from that of the original reference signal, and transmitted through the same resource region, is considered with regard to the index of the ZC sequences.

More specifically, in the following examples, the sequences having the length of 1 RB, 2 RB and 3 RB is considered. And, let us presume that the sequences having the length of 1 RB and 2 RB are generated by the cyclic extension of the ZC sequence having the length given by the largest prime number which is less than a corresponding resource block size. And, let us presume that the sequence having the length of 3 RB is generated by the truncated sequence generation method. That is, the sequences can be generated to have the corresponding resource block size based on the prime number length by one of the above 3 generation methods.

First, consider the case when the sequence having 1 RB length and the sequence having 2 RB length is overlapped in the same resource region. The sequence having 1 RB length and the sequence having 2 RB length can be expressed as follows.

$\begin{matrix} {{{{g_{1\;{RB}}\left( {k;s_{1}} \right)} = e^{{- j}\frac{\pi}{N_{1}}s_{1}{k{({k + 1})}}}},{k = 0},\ldots\mspace{14mu},{N - 1}}{{{g_{2\;{RB}}\left( {k;s_{2}} \right)} = e^{{- j}\frac{\pi}{N_{2}}s_{2}{k{({k + 1})}}}},{k = 0},\ldots\mspace{14mu},{{2N} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack \end{matrix}$

Here, s₁ and s₂ indicate the indexes which are relative prime to the sequence length (N or 2N). In this example, for the sequences having 1 RB length and 2 RB length are generated using the cyclic extension method, s₁ can be 1, 2, . . . , 10 and s₂ can be 1, 2, . . . , 22. And, N₁ may be 11, and N₂ may be 23.

Based on this, the cross correlation value (c(d; s₁, s₂)) generated when the sequence with 1 RB length is overlapped with the sequence with 2 RB length in the first 12 subcarriers region of the sequence with 2 RB length can be expressed as follows.

$\begin{matrix} {{{c\left( {d;{s_{1} \cdot s_{2}}} \right)} = {\sum\limits_{k = 0}^{N - 1}\;{{g_{1,{RB}}\left( {k;s_{1}} \right)}{g_{2\;{RB}}^{*}\left( {{k + d};s_{2}} \right)}}}}\mspace{14mu}{For}{{d = 0},\begin{matrix} {{c\left( {{0;s_{1}},s_{2}} \right)} = {\sum\limits_{k = 0}^{N - 1}\;{{\exp\left( {{- j}\frac{\pi}{N_{1}}s_{1}{{mod}\left( {k,{N - 1}} \right)}\left( {{{mod}\left( {k,{N - 1}} \right)} + 1} \right)} \right)}\exp}}} \\ {\left( {j\frac{\pi}{N_{1}}s_{2}{{mod}\left( {k,{{2N} - 1}} \right)}\left( {{{mod}\left( {k,{{2N} - 1}} \right)} + 1} \right)} \right)} \\ {= {\left\lbrack {\sum\limits_{k = 0}^{10}\;{\exp\left\{ {j\;\pi\;{k\left( {k + 1} \right)}\left( {\frac{s_{2}}{23} - \frac{s_{1}}{11}} \right)} \right\}}} \right\rbrack + {\exp\left( {j\frac{\pi}{23}{s_{2} \cdot 11 \cdot 12}} \right)}}} \end{matrix}}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack \end{matrix}$

According to the equation 7, it can be understood that if the combination of sequence indexes (s₁ and s₂) meet the condition that the term of

$\left( {\frac{s_{2}}{23} - \frac{s_{1}}{11}} \right)$ becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation.

Therefore, one embodiment of the present invention proposes to perform grouping the sequences into groups such that the sequences contained in each group have the high cross correlation relation with each other. And, if 1 RB length sequence and 2 RB length sequence are considered, grouping the combination of sequence indexes which meets the condition that the term of

$\left( {\frac{s_{2}}{23} - \frac{s_{1}}{11}} \right)$ becomes close to zero is proposed.

But, to determine more general condition for the grouping sequences, let us consider some other examples.

When 1 RB sequence is overlapped in the last 12 subcarriers region of the 2 RB sequence, the cross correlation value (c(d; s₁, s₂)) of the two sequences can be expressed as follows.

$\begin{matrix} {\mspace{79mu}{{{c\left( {d;{s_{1} \cdot s_{2}}} \right)} = {\sum\limits_{k = 0}^{N - 1}\;{{g_{1,{RB}}\left( {k;s_{1}} \right)}{g_{2\;{RB}}^{*}\left( {{k + 12 + d};s_{2}} \right)}}}}\mspace{14mu}\mspace{20mu}{For}\mspace{20mu}{{d = 0},\begin{matrix} {{c\left( {{d;s_{1}},s_{2}} \right)} = {\sum\limits_{k = 0}^{N - 1}\;{{\exp\left( {{- j}\frac{\pi}{N_{1}}s_{1}{{mod}\left( {k,{N - 1}} \right)}\left( {{{mod}\left( {k,{N - 1}} \right)} + 1} \right)} \right)}\exp}}} \\ {\left( {j\frac{\pi}{N_{1}}s_{2}{{mod}\left( {{k + 12},{{2N} - 1}} \right)}\left( {{{mod}\left( {{k + 12},{{2N} - 1}} \right)} + 1} \right)} \right)} \\ {= {\left\lbrack {\sum\limits_{k = 0}^{10}\;{\exp\left\{ {{j\;\pi\;{k\left( {k + 1} \right)}\left( {\frac{s_{2}}{23} - \frac{s_{1}}{11}} \right)} + {\frac{s_{2}}{23} \cdot 12 \cdot \left( {{2k} + 13} \right)}} \right\}}} \right\rbrack + 1}} \end{matrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \end{matrix}$

According to the equation 8, it can also concluded that if the combination of sequence indexes (s₁ and s₂) meet the condition that the term of

$\left( {\frac{s_{2}}{23} - \frac{s_{1}}{11}} \right)$ becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. So, if 1 RB length sequence and 2 RB length sequence are considered, the position where the overlapping is occurred is not change the grouping condition.

Next, let us consider the case when the 1 RB length sequence and the 3 RB length sequence are overlapped in the same resource region.

First of all, the 1 RB length sequence and the 3 RB length sequence can be expressed as follows.

$\begin{matrix} {{{{g_{1\;{RB}}\left( {k;s_{1}} \right)} = e^{{- j}\frac{\pi}{N_{1}}s_{1}{k{({k + 1})}}}},{k = 0},\ldots\mspace{14mu},{N - 1}}{{g_{3\;{RB}}\left( {k;s_{3}} \right)} = e^{{- j}\frac{\pi}{N_{3}}s_{3}{k{({k + 1})}}}},{k = 0},\ldots\mspace{14mu},{{3N} - 1}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack \end{matrix}$

Here, s₁ and s₃ indicate the indexes which are relative prime to the sequence length (N or 3N). In this example, for the 1 RB length sequences is generated using the cyclic extension method and the 3 RB length sequence is generated using the truncated sequence generation method, s₁ can be 1, 2, . . . , 10 and s₂ can be 1, 2, . . . , 36. And, N₁ may be 11, and N₂ may be 37.

Based on this, if the 1 RB length sequence is overlapped in the first 12 subcarriers region of the 3 RB length sequence, the cross correlation value between the two sequences can be expressed as follows.

$\begin{matrix} {{{c\left( {d;{s_{1} \cdot s_{2}}} \right)} = {\sum\limits_{k = 0}^{N - 1}\;{{g_{1,{RB}}\left( {k;s_{1}} \right)}{g_{2\;{RB}}^{*}\left( {{k + d};s_{2}} \right)}}}}\mspace{14mu}{For}{{d = 0},\begin{matrix} {{c\left( {{0;s_{1}},s_{2}} \right)} = {\sum\limits_{k = 0}^{N - 1}\;{{\exp\left( {{- j}\frac{\pi}{N_{1}}s_{1}{{mod}\left( {k,{N - 1}} \right)}\left( {{{mod}\left( {k,{N - 1}} \right)} + 1} \right)} \right)}\exp}}} \\ {\left( {j\frac{\pi}{N_{3}}s_{3}{k\left( {k + 1} \right)}} \right)} \\ {= {\left\lbrack {\sum\limits_{k = 0}^{10}\;{\exp\left\{ {j\;\pi\;{k\left( {k + 1} \right)}\left( {\frac{s_{3}}{37} - \frac{s_{1}}{11}} \right)} \right\}}} \right\rbrack + {\exp\left( {j\frac{\pi}{37}{s_{3} \cdot 11 \cdot 12}} \right)}}} \end{matrix}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack \end{matrix}$

According to the equation 10, it can be understood that if the combination of sequence indexes (s₁ and s₃) meet the condition that the term of

$\left( {\frac{s_{3}}{37} - \frac{s_{1}}{11}} \right)$ becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. Therefore, if 1 RB length sequence and 3 RB length sequence are considered, grouping the combination of sequence indexes which meets the condition that the term of

$\left( {\frac{s_{3}}{37} - \frac{s_{1}}{11}} \right)$ becomes close to zero is proposed.

And, to certify the relation with the position where the overlapping is occurred, let us consider the case when the 1 RB length sequence is overlapped in the second 12 subcarriers region of the 3 RB length sequence. In this case, the cross correlation value between these two sequences can be expressed as follows.

                                     [Equation  11] $\mspace{85mu}{{c\left( {{d;s_{1}},s_{3}} \right)} = {\sum\limits_{k = 0}^{N - 1}{{g_{1\mspace{11mu}{RB}}\left( {k;s_{1}} \right)}{g_{1\;{RB}}^{*}\left( {{k + 12 + d};s_{3}} \right)}}}}$ $\mspace{79mu}{{{{For}\mspace{14mu} d} = 0},\begin{matrix} {{c\left( {{0;s_{1}},s_{3}} \right)} = {\sum\limits_{k = 0}^{N - 1}{\exp\left( {{- j}\frac{\pi}{N_{1}}s_{1}{{mod}\left( {k,{N - 1}} \right)}\left( {{{mod}\left( {k,{N - 1}} \right)} + 1} \right)} \right)}}} \\ {\exp\left( {j\frac{\pi}{N_{3}}{s_{3}\left( {k + 12} \right)}\left( {k + 13} \right)} \right)} \\ {= {\left\lbrack {\sum\limits_{k = 0}^{10}{\exp\left\lbrack {j\;\pi\left\{ {{{k\left( {k + 1} \right)}\left( {\frac{s_{3}}{37} - \frac{s_{1}}{11}} \right)} + {\frac{s_{2}}{37} \cdot 12 \cdot \left( {{2k} + 13} \right)}} \right\}} \right\rbrack}} \right\rbrack +}} \\ {\exp\left( {j\frac{\pi}{37}{s_{3} \cdot 23 \cdot 24}} \right)} \end{matrix}}$

And, when the 1 RB length sequence overlapped in the last 12 subcarrier region of the 3 RB length sequence, the cross correlation value can be expressed as follows.

                                     [Equation  12] $\mspace{20mu}{{c\left( {{d;s_{1}},s_{3}} \right)} = {\sum\limits_{k = 0}^{N - 1}{{g_{1\;{RB}}\left( {k;s_{1}} \right)}{g_{3\;{RB}}^{*}\left( {{k + 24 + d};s_{3}} \right)}}}}$ $\mspace{20mu}{{{{For}\mspace{14mu} d} = 0},\begin{matrix} {{c\left( {{0;s_{1}},s_{3}} \right)} = {\sum\limits_{k = 0}^{N - 1}{\exp\left( {{- j}\frac{\pi}{N_{1}}s_{1}{{mod}\left( {k,{N - 1}} \right)}\left( {{{mod}\left( {k,{N - 1}} \right)} + 1} \right)} \right)}}} \\ {\exp\left( {j\frac{\pi}{N_{3}}{s_{3}\left( {k + 24} \right)}\left( {k + 25} \right)} \right)} \\ {= {\left\lbrack {\sum\limits_{k = 0}^{10}{\exp\left\lbrack {j\;\pi\left\{ {{{k\left( {k + 1} \right)}\left( {\frac{s_{3}}{37} - \frac{s_{1}}{11}} \right)} + {\frac{s_{2}}{37} \cdot 24 \cdot \left( {{2k} + 25} \right)}} \right\}} \right\rbrack}} \right\rbrack +}} \\ {\exp\left( {j\frac{\pi}{37}{s_{3} \cdot 35 \cdot 36}} \right)} \end{matrix}}$

According to the equations 11 and 12, it can also concluded that if the combination of sequence indexes (s₁ and s₃) meet the condition that the term of

$\left( {\frac{s_{3}}{37} - \frac{s_{1}}{11}} \right)$ becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. So, if 1 RB length sequence and 3 RB length sequence are considered, the position where the overlapping is occurred is not change the grouping condition.

According to the above examples, the present embodiment proposes to perform grouping sequences such that two sequence indexes among all the sequence indexes grouped into the same group meet the condition that the term (s₂/N₂−s₁/N₁) becomes close to zero, when the two sequences having the length of N₁ and N₂ are considered. Here, N₁ and N₂ can be maximum relative prime numbers which are less than the resultant reference signal sequence. And, s₁ and s₂ mean the root indexes of the ZC sequences, and can be selected among the ranges of 1˜(N₁−1) and 1˜(N₂−1) respectively.

Based on this concept, let's consider more general grouping method considering various length sequences.

FIGS. 3 to 5 show conceptual diagrams of grouping sequences according to one embodiment of this invention.

According to this embodiment, among various length sequences such as 1 RB, 2 RB, 3 RB . . . as shown in the FIG. 3, the sequences whose indexes meet the high cross correlation condition as stated above may be grouped into the same group. And, each of the sequence groups can be allocated to the same cell or node B.

Generally, FDM is done with the unit of cell or Node B, so the inference caused by using the sequences having difference length can be minimized within one cell or Node B. So, by allocating the sequences having the high cross correlation relation to the same cell or Node B, the inter cell interference caused by using the different length sequences can be minimized.

And, another embodiment of this invention proposes to perform grouping such that each of the groups contains at least one sequence of each length. By doing so, if the sequence group is allocated to the same cell or Node B, UE(s) located in that cell or Node B can be supported to use various length reference signal sequence. But specific grouping method can be variously defined.

First, the number of sequences allocated to one group can be proportional to the number of RBs which corresponds to the reference signal sequence length. In FIG. 3, one sequence for 1 RB length sequence, two sequences for 2 RB length sequence, 3 sequences for 3 RB length sequence, and so on, are grouped.

Second, the number of sequences allocated to one group can be a constant number. In FIG. 4, one sequence for each RB length sequence is grouped to the same group.

And, the present embodiment can be defined to perform grouping such that the number of sequences allocated to one group is neither proportional to the sequence length nor remain constant. FIG. 5 shows an example of grouping sequence such that one sequence for 1 RB length sequence, 2 sequences for 2 RB length sequence, 2 sequences for 3 RB length sequence, and 3 sequences for 4 RB length sequence, and so on, are grouped into one group.

As like the above, if each group contains at least one sequence of each RB length, the maximum number of sequence per group can be defined. When the maximum number of sequence per group is defined, a method for selecting root index of the ZC sequence within the sequence number limit can be defined as follows.

If one sequence is selected per each RB length sequence, and if one specific sequence with the index of s₁ and the length of N₁ is already selected for that group, one sequence per (having index of s₂) each RB length can be selected, of which index make the term of (s₂/N₂−s₁/N₁) to be closest to zero, where N₂ is the sequence length corresponding to the considered RB length. And, if 2 sequences are selected per certain RB length sequence, and if one specific sequence with the index of s₁ and the length of N₁ is already selected for that group, two sequences per that RB length can be selected to make the term of (s₂/N₂−s₁/N₁) to be close to zero. This can be more generalized to the maximum sequence number of “x” per each RB length.

And, another grouping method can be defined as follows. If one sequence is selected per each RB length sequence, and if one specific sequence with the index of s₁ and the length of N₁ is already selected for that group, first, select certain number (y) of sequences among sequences which make the term (s₂/N₂−s₁/N₁) to be close to certain value, and then, select one sequence among the y sequences which has high cross correlation relation with the sequence having the index of s₁. And, if 2 sequences are selected per certain RB length sequence, and if one specific sequence with the index of s₁ and the length of N₁ is already selected for that group, first, select certain number (y) of sequences among sequences which make the term (s₂/N₂−s₁/N₁) to be close to certain value, and then, select two sequences among the y sequences which have high cross correlation relation with the sequence having the index of s₁. This can be more generalized to the maximum sequence number of “x” per each RB length.

In the above examples, one specific sequence with the index of s₁ and the length of N₁ is firstly selected and becomes the reference for selecting rest of the sequence. This reference sequence can be defined to be 1 RB length sequence, 2 RB length sequence, 3 RB length sequence, and so on. But In the following explanation, let us presume that the reference sequence is the 3 RB length sequence. And, because the number of sequence indexes per 3 RB length is 30, the number of groups for grouping sequence according to this embodiment of the invention can be 30.

Considering that the number of root indexes for 3 RB length sequence is 30, the number of root index selected for certain group can be determined as follows. round(the number of root index for certain RB length sequence/30)  [Equation 13]

Here, “round (z)” is a function of rounding off to a nearest integer nearest to z.

By the equation 13, for 3 RB and 4 RB lengths, 1 sequence can be selected. And, for 5 RB˜6 RB lengths, 2 sequence can be selected. Further, for the length greater than the 6 RB length, 3 or more sequence can be selected, respectively. And, according to one embodiment of this invention, sequence with the length less than 3 RB length can be differently defined, such as not using ZC sequence. By doing so, the number of sequences selected for 1 RB length and 2 RB length can be determined to 1.

To summarize, according to this embodiment, the number of sequence per groups can be defined as follows. {1RB,2RB,3RB,4RB,5RB,6RB,8RB,9RB,10RB,12RB,15RB,16RB,18RB,20RB, 24RB,25RB, . . . }={1,1,1,1,2,2,3,3,4,5,6,6,7,8,9,9, . . . }  [Equation 14]

Based on this, the following tables 1-5 show an example of sequence grouping such that each group contains the number of sequences according to the equation 14, and the sequences selected per each group satisfy the high cross correlation relation as stated above.

TABLE 1 Groupindex based on 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 1 1 2 2 1 2 3 3 2 4 3 4 2 2 2 3 4 3 5 4 6 5 7 7 6 8 3 3 5 6 5 7 6 9 8 10 11 9 4 4 6 8 7 9 10 11 12 14 13 15 5 5 8 10 9 11 12 14 15 13 17 18 16 6 6 9 11 12 14 13 17 18 16 21 20 22 7 7 11 13 14 16 17 20 21 19 24 25 23 8 8 12 15 16 18 19 23 22 24 28 27 29 9 9 14 17 18 21 20 26 25 27 31 32 30 10 10 15 19 23 22 29 28 30 35 34 36 11 11 17 21 25 26 32 31 38 37 39 12 12 18 23 22 27 28 34 35 41 42 40 13 13 20 25 24 30 29 37 38 36 45 44 46 14 14 21 27 26 32 33 40 41 39 48 49 47 15 15 23 29 28 34 35 43 44 42 52 51 53 16 16 24 30 31 37 36 46 45 47 55 56 54 17 17 26 32 33 39 38 49 48 50 59 58 60 18 18 27 34 35 41 42 52 51 53 62 63 61 19 19 29 36 37 44 43 55 54 66 65 67 20 20 30 38 46 45 57 58 69 70 68 21 21 32 40 48 49 60 61 59 72 73 71 22 22 33 42 41 50 51 63 64 62 76 75 77 23 23 35 44 43 53 52 66 67 65 79 80 78 24 24 36 46 45 55 54 69 68 70 83 82 84 25 25 38 48 47 57 58 72 71 73 86 87 85 26 26 39 49 50 60 59 75 74 76 90 89 91 27 27 41 51 52 62 61 78 77 93 94 92 28 28 42 53 54 64 65 80 81 97 96 98 29 29 44 55 56 66 67 83 84 82 100 101 99 30 30 45 57 58 69 68 86 87 85 104 103 105

TABLE 2 Groupindex based on 3RBs 10RB 12RB 15RB 1 4 3 5 2 4 5 3 6 2 6 5 7 4 8 3 2 7 8 6 9 8 10 7 12 11 13 10 14 9 3 11 10 12 13 14 12 15 17 18 16 19 15 20 4 15 14 16 13 18 17 19 16 23 24 22 25 21 5 18 19 17 22 23 21 24 29 28 30 27 31 6 22 21 23 27 26 28 25 35 34 36 33 37 32 7 26 25 27 24 31 32 30 33 40 41 39 42 38 43 8 29 30 28 36 35 37 34 46 47 45 48 44 9 33 32 34 40 41 39 42 52 51 53 50 54 10 36 37 35 38 45 44 46 43 58 57 59 56 60 55 11 40 41 39 49 50 48 51 64 63 65 62 66 61 12 44 43 45 54 53 55 52 69 70 68 71 67 72 13 47 48 46 49 58 59 57 60 75 76 74 77 73 14 51 52 50 63 62 64 61 81 80 82 79 83 15 55 54 56 67 68 66 69 87 86 88 85 89 84 16 58 59 57 72 71 73 70 92 93 91 94 90 95 17 62 61 63 76 77 75 78 98 99 97 100 96 18 66 65 67 64 81 80 82 79 104 103 105 102 106 19 69 70 68 85 86 84 87 110 109 111 108 112 107 20 73 72 74 90 89 91 88 115 116 114 117 113 118 21 77 76 78 75 94 95 93 96 121 122 120 123 119 124 22 80 81 79 99 98 100 97 127 128 126 129 125 23 84 83 85 103 104 102 105 133 132 134 131 135 24 87 88 86 89 108 107 109 106 139 138 140 137 141 136 25 91 92 90 112 113 111 114 144 145 143 146 142 147 26 95 94 96 117 116 118 115 150 151 149 152 148 27 98 99 97 100 121 122 120 123 156 155 157 154 158 28 102 103 101 126 125 127 124 162 161 163 160 164 159 29 106 105 107 130 131 129 132 167 168 166 169 165 170 30 109 110 108 111 135 134 136 133 137 173 174 172 175 171 176

TABLE 3 Groupindex based on 3RBs 16RB 18RB 1 6 7 5 8 4 9 7 6 8 5 9 4 10 2 12 13 11 14 10 15 14 13 15 12 16 11 17 3 18 19 17 20 16 21 20 21 19 22 18 23 17 4 25 24 26 23 27 22 27 28 26 29 25 30 24 5 31 30 32 29 33 28 34 35 33 36 32 37 31 6 37 36 38 35 39 34 41 40 42 39 43 38 44 7 43 44 42 45 41 46 48 47 49 46 50 45 51 8 49 50 48 51 47 52 54 55 53 56 52 57 51 9 55 56 54 57 53 58 61 62 60 63 59 64 58 10 62 61 63 60 64 59 68 69 67 70 66 71 65 11 68 67 69 66 70 65 75 74 76 73 77 72 78 12 74 73 75 72 76 71 82 81 83 80 84 79 85 13 80 81 79 82 78 83 88 89 87 90 86 91 85 14 86 87 85 88 84 89 95 96 94 97 93 98 92 15 92 93 91 94 90 95 102 103 101 104 100 105 99 16 99 98 100 97 101 96 109 108 110 107 111 106 112 17 105 104 106 103 107 102 116 115 117 114 118 113 119 18 111 110 112 109 113 108 123 122 124 121 125 120 126 19 117 118 116 119 115 120 129 130 128 131 127 132 126 20 123 124 122 125 121 126 136 137 135 138 134 139 133 21 129 130 128 131 127 132 143 142 144 141 145 140 146 22 136 135 137 134 138 133 150 149 151 148 152 147 153 23 142 141 143 140 144 139 157 156 158 155 159 154 160 24 148 147 149 146 150 145 163 164 162 165 161 166 160 25 154 155 153 156 152 157 170 171 169 172 168 173 167 26 160 161 159 162 158 163 177 176 178 175 179 174 180 27 166 167 165 168 164 169 184 183 185 182 186 181 187 28 173 172 174 171 175 170 191 190 192 189 193 188 194 29 179 178 180 177 181 176 197 198 196 199 195 200 194 30 185 184 186 183 187 182 204 205 203 206 202 207 201

TABLE 4 Groupindex based on 3RBs 20RB 24RB 1 8 7 9 6 10 5 11 4 9 10 8 11 7 12 6 13 5 2 15 16 14 17 13 18 12 19 18 19 17 20 16 21 15 22 14 3 23 24 22 25 21 26 20 27 28 26 29 25 30 24 31 23 4 31 30 32 29 33 28 34 37 36 38 35 39 34 40 33 41 5 39 38 40 37 41 36 42 35 46 45 47 44 48 43 49 42 50 6 46 47 45 48 44 49 43 55 54 56 53 57 52 58 51 59 7 54 53 55 52 56 51 57 64 63 65 62 66 61 67 60 68 8 62 61 63 60 64 59 65 58 73 74 72 75 71 76 70 77 69 9 69 70 68 71 67 72 66 73 82 83 81 84 80 85 79 86 78 10 77 78 76 79 75 80 74 91 92 90 93 89 94 88 95 87 11 85 84 86 83 87 82 88 100 101 99 102 98 103 97 104 96 12 93 92 94 91 95 90 96 89 110 109 111 108 112 107 113 106 114 13 100 101 99 102 98 103 97 119 118 120 117 121 116 122 115 123 14 108 107 109 106 110 105 111 128 127 129 126 130 125 131 124 132 15 116 115 117 114 118 113 119 112 137 136 138 135 139 134 140 133 141 16 123 124 122 125 121 126 120 127 146 147 145 148 144 149 143 150 142 17 131 132 130 133 129 134 128 155 156 154 157 153 158 152 159 151 18 139 138 140 137 141 136 142 164 165 163 166 162 167 161 168 160 19 146 147 145 148 144 149 143 150 173 174 172 175 171 178 170 177 169 20 154 155 153 156 152 157 151 183 182 184 181 185 180 186 179 187 21 162 161 163 160 164 159 165 192 191 193 190 194 189 195 188 196 22 170 169 171 168 172 167 173 166 201 200 202 199 203 198 204 197 205 23 177 178 176 179 175 180 174 181 210 209 211 208 212 207 213 206 214 24 185 186 184 187 183 188 182 219 220 218 221 217 222 216 223 215 25 193 192 194 191 195 190 196 228 229 227 230 226 231 225 232 224 26 200 201 199 202 198 203 197 204 237 238 236 239 235 240 234 241 233 27 208 209 207 210 206 211 205 246 247 245 248 244 249 243 250 242 28 216 215 217 214 218 213 219 256 255 257 254 258 253 259 252 260 29 224 223 225 222 226 221 227 220 265 264 266 263 267 262 268 261 269 30 231 232 230 233 229 234 228 235 274 273 275 272 276 271 277 270 278

TABLE 5 Group- index based- on 3RBs 25RBs 1 9 10 8 11 7 12 6 13 5 2 19 18 20 17 21 16 22 15 23 3 28 29 27 30 26 31 25 32 24 4 38 37 39 36 40 35 41 34 42 5 47 48 46 49 45 50 44 51 43 6 57 56 58 55 59 54 60 53 61 7 66 67 65 68 64 69 63 70 62 8 76 75 77 74 78 73 79 72 80 9 85 86 84 87 83 88 82 89 81 10 95 94 96 93 97 92 98 91 99 11 104 103 105 102 106 101 107 100 108 12 113 114 112 115 111 116 110 117 109 13 123 122 124 121 125 120 126 119 127 14 132 133 131 134 130 135 129 136 128 15 142 141 143 140 144 139 145 138 146 16 151 152 150 153 149 154 148 155 147 17 161 160 162 159 163 158 164 157 165 18 170 171 169 172 168 173 167 174 166 19 180 179 181 178 182 177 183 176 184 20 189 190 188 191 187 192 186 193 185 21 198 199 197 200 196 201 195 202 194 22 208 207 209 206 210 205 211 204 212 23 217 218 216 219 215 220 214 221 213 24 227 226 228 225 229 224 230 223 231 25 236 237 235 238 234 239 233 240 232 26 246 245 247 244 248 243 249 242 250 27 255 256 254 257 253 258 252 259 251 28 265 264 266 263 267 262 268 261 269 29 274 275 273 276 272 277 271 278 270 30 284 283 285 282 286 281 287 280 288

In the tables 1˜5, 1 RB and 2 RB length sequence are not shown because 1 RB and 2 RB length sequence are differently defined.

And, in another example, considering that the number of root indexes for 3 RB length sequence is 30, the number of root index selected for certain group can be determined as follows. floor(the number of root index for certain RB length sequence/30)  [Equation 15]

Here, floor (z) is a function of making the greatest integer not greater than z.

By the equation 15, for 3˜5 RB lengths, 1 sequence can be selected. And, for 6˜8 RB lengths, 2 sequence can be selected. Further, for the length greater than the 9 RB length, 3 or more sequence can be selected, respectively. And, according to one embodiment of this invention, sequence with the length less than 3 RB length can be differently defined, such as not using ZC sequence. By doing so, the number of sequences selected for 1 RB length and 2 RB length can be determined to 1.

To summarize, according to this embodiment, the number of sequence per groups can be defined as follows. {1RB,2RB,3RB,4RB,5RB,6RB,8RB,9RB,10RB,12RB,15RB,16RB,18RB,20RB, 24RB,25RB, . . . }={1,1,1,1,1,2,2,3,3,4,5,6,7,7,9,9, . . . }  [Equation 16]

Based on this, the following tables 6-8 show an example of sequence grouping such that each group contains the number of sequences according to the equation 16, and the sequences selected per each group satisfy the high cross correlation relation as stated above.

TABLE 6 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 1 1 2 2 2 3 3 2 3 4 2 4 3 5 2 2 3 4 5 4 6 5 7 6 8 7 8 6 3 3 5 6 7 6 9 8 10 11 9 11 10 12 4 4 6 8 9 10 11 12 14 13 15 15 14 16 5 5 8 10 11 12 14 15 17 18 16 18 19 17 6 6 9 11 14 13 17 18 21 20 22 22 21 23 7 7 11 13 16 17 20 21 24 25 23 26 25 27 8 8 12 15 18 19 23 22 28 27 29 29 30 28 9 9 14 17 21 20 26 25 31 32 30 33 32 34 10 10 15 19 23 22 29 28 35 34 36 36 37 35 11 11 17 21 25 26 32 31 38 37 39 40 41 39 12 12 18 23 27 28 34 35 41 42 40 44 43 45 13 13 20 25 30 29 37 38 45 44 46 47 48 46 14 14 21 27 32 33 40 41 48 49 47 51 52 50 15 15 23 29 34 35 43 44 52 51 53 55 54 56 16 16 24 30 37 36 46 45 55 56 54 58 59 57 17 17 26 32 39 38 49 48 59 58 60 62 61 63 18 18 27 34 41 42 52 51 62 63 61 66 65 67 19 19 29 36 44 43 55 54 66 65 67 69 70 68 20 20 30 38 46 45 57 58 69 70 68 73 72 74 21 21 32 40 48 49 60 61 72 73 71 77 76 78 22 22 33 42 50 51 63 64 76 75 77 80 81 79 23 23 35 44 53 52 66 67 79 80 78 84 83 85 24 24 36 46 55 54 69 68 83 82 84 87 88 86 25 25 38 48 57 58 72 71 86 87 85 91 92 90 26 26 39 49 60 59 75 74 90 89 91 95 94 96 27 27 41 51 62 61 78 77 93 94 92 98 99 97 28 28 42 53 64 65 80 81 97 96 98 102 103 101 29 29 44 55 66 67 83 84 100 101 99 106 105 107 30 30 45 57 69 68 86 87 104 103 105 109 110 108 Gr. Idx 3RBs 12RB 15RB  1 4 5 3 6 6 5 7 4 8  2 9 8 10 7 12 11 13 10 14  3 13 14 12 15 17 18 16 19 15  4 18 17 19 16 23 24 22 25 21  5 22 23 21 24 29 28 30 27 31  6 27 26 28 25 35 34 36 33 37  7 31 32 30 33 40 41 39 42 38  8 36 35 37 34 46 47 45 48 44  9 40 41 39 42 52 51 53 50 54 10 45 44 46 43 58 57 59 56 60 11 49 50 48 51 64 63 65 62 66 12 54 53 55 52 69 70 68 71 67 13 58 59 57 60 75 76 74 77 73 14 63 62 64 61 81 80 82 79 83 15 67 68 66 69 87 86 88 85 89 16 72 71 73 70 92 93 91 94 90 17 76 77 75 78 98 99 97 100 96 18 81 80 82 79 104 103 105 102 106 19 85 86 84 87 110 109 111 108 112 20 90 89 91 88 115 116 114 117 113 21 94 95 93 96 121 122 120 123 119 22 99 98 100 97 127 128 126 129 125 23 103 104 102 105 133 132 134 131 135 24 108 107 109 106 139 138 140 137 141 25 112 113 111 114 144 145 143 146 142 26 117 116 118 115 150 151 149 152 148 27 121 122 120 123 156 155 157 154 158 28 126 125 127 124 162 161 163 160 164 29 130 131 129 132 167 168 166 169 165 30 135 134 136 133 173 174 172 175 171

TABLE 7 Gr. Idx 3RBs 16RB 18RB 20RB 1 6 7 5 8 4 9 7 6 8 5 9 4 10 8 7 9 6 10 5 11 2 12 13 11 14 10 15 14 13 15 12 16 11 17 15 16 14 17 13 18 12 3 18 19 17 20 16 21 20 21 19 22 18 23 17 23 24 22 25 21 26 20 4 25 24 26 23 27 22 27 28 26 29 25 30 24 31 30 32 29 33 28 34 5 31 30 32 29 33 28 34 35 33 36 32 37 31 39 38 40 37 41 36 42 6 37 36 38 35 39 34 41 40 42 39 43 38 44 46 47 45 48 44 49 43 7 43 44 42 45 41 46 48 47 49 46 50 45 51 54 53 55 52 56 51 57 8 49 50 48 51 47 52 54 55 53 56 52 57 51 62 61 63 60 64 59 65 9 55 56 54 57 53 58 61 62 60 63 59 64 58 69 70 68 71 67 72 66 10 62 61 63 60 64 59 68 69 67 70 66 71 65 77 78 76 79 75 80 74 11 68 67 69 66 70 65 75 74 76 73 77 72 78 85 84 86 83 87 82 88 12 74 73 75 72 76 71 82 81 83 80 84 79 85 93 92 94 91 95 90 96 13 80 81 79 82 78 83 88 89 87 90 86 91 85 100 101 99 102 98 103 97 14 86 87 85 88 84 89 95 96 94 97 93 98 92 108 107 109 106 110 105 111 15 92 93 91 94 90 95 102 103 101 104 100 105 99 116 115 117 114 118 113 119 16 99 98 100 97 101 96 109 108 110 107 111 106 112 123 124 122 125 121 126 120 17 105 104 106 103 107 102 116 115 117 114 118 113 119 131 132 130 133 129 134 128 18 111 110 112 109 113 108 123 122 124 121 125 120 126 139 138 140 137 141 136 142 19 117 118 116 119 115 120 129 130 128 131 127 132 126 146 147 145 148 144 149 143 20 123 124 122 125 121 126 136 137 135 138 134 139 133 154 155 153 156 152 157 151 21 129 130 128 131 127 132 143 142 144 141 145 140 146 162 161 163 160 164 159 165 22 136 135 137 134 138 133 150 149 151 148 152 147 153 170 169 171 168 172 167 173 23 142 141 143 140 144 139 157 156 158 155 159 154 160 177 178 176 179 175 180 174 24 148 147 149 146 150 145 163 164 162 165 161 166 160 185 186 184 187 183 188 182 25 154 155 153 156 152 157 170 171 169 172 168 173 167 193 192 194 191 195 190 196 26 160 161 159 162 158 163 177 176 178 175 179 174 180 200 201 199 202 198 203 197 27 166 167 165 168 164 169 184 183 185 182 186 181 187 208 209 207 210 206 211 205 28 173 172 174 171 175 170 191 190 192 189 193 188 194 216 215 217 214 218 213 219 29 179 178 180 177 181 176 197 198 196 199 195 200 194 224 223 225 222 226 221 227 30 185 184 186 183 187 182 204 205 203 206 202 207 201 231 232 230 233 229 234 228

TABLE 8 Gr. Idx 3RBs 24RB 25RBs 1 9 10 8 11 7 12 6 13 5 9 10 8 11 7 12 6 13 5 2 18 19 17 20 16 21 15 22 14 19 18 20 17 21 16 22 15 23 3 27 28 26 29 25 30 24 31 23 28 29 27 30 26 31 25 32 24 4 37 36 38 35 39 34 40 33 41 38 37 39 36 40 35 41 34 42 5 46 45 47 44 48 43 49 42 50 47 48 46 49 45 50 44 51 43 6 55 54 56 53 57 52 58 51 59 57 56 58 55 59 54 60 53 61 7 64 63 65 62 66 61 67 60 68 66 67 65 68 64 69 63 70 62 8 73 74 72 75 71 76 70 77 69 76 75 77 74 78 73 79 72 80 9 82 83 81 84 80 85 79 86 78 85 86 84 87 83 88 82 89 81 10 91 92 90 93 89 94 88 95 87 95 94 96 93 97 92 98 91 99 11 100 101 99 102 98 103 97 104 96 104 103 105 102 106 101 107 100 108 12 110 109 111 108 112 107 113 106 114 113 114 112 115 111 116 110 117 109 13 119 118 120 117 121 116 122 115 123 123 122 124 121 125 120 126 119 127 14 128 127 129 126 130 125 131 124 132 132 133 131 134 130 135 129 136 128 15 137 136 138 135 139 134 140 133 141 142 141 143 140 144 139 145 138 146 16 146 147 145 148 144 149 143 150 142 151 152 150 153 149 154 148 155 147 17 155 156 154 157 153 158 152 159 151 161 160 162 159 163 158 164 157 165 18 164 165 163 166 162 167 161 168 160 170 171 169 172 168 173 167 174 166 19 173 174 172 175 171 176 170 177 169 180 179 181 178 182 177 183 176 184 20 183 182 184 181 185 180 186 179 187 189 190 188 191 187 192 186 193 185 21 192 191 193 190 194 189 195 188 196 198 199 197 200 196 201 195 202 194 22 201 200 202 199 203 198 204 197 205 208 207 209 206 210 205 211 204 212 23 210 209 211 208 212 207 213 206 214 217 218 216 219 215 220 214 221 213 24 219 220 218 221 217 222 216 223 215 227 226 228 225 229 224 230 223 231 25 228 229 227 230 226 231 225 232 224 236 237 235 238 234 239 233 240 232 26 237 238 236 239 235 240 234 241 233 246 245 247 244 248 243 249 242 250 27 246 247 245 248 244 249 243 250 242 255 256 254 257 253 258 252 259 251 28 256 255 257 254 258 253 259 252 260 265 264 266 263 267 262 268 261 269 29 265 264 266 263 267 262 268 261 269 274 275 273 276 272 277 271 278 270 30 274 273 275 272 276 271 277 270 278 284 283 285 282 286 281 287 280 288

As like the tables 1˜5, in the tables 6˜8, 1 RB and 2 RB length sequence are not shown because 1 RB and 2 RB length sequence are differently defined.

In another embodiment of this invention, the maximum number of sequences per each group can be predetermined for various reasons. The following tables 9 and 10 show the example of the case when the maximum number of sequences per group is limited to 5 sequences.

TABLE 9 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 1 1 2 2 2 3 3 2 3 4 2 4 3 5 2 2 3 4 5 4 6 5 7 6 8 7 8 6 3 3 5 6 7 6 9 8 10 11 9 11 10 12 4 4 6 8 9 10 11 12 14 13 15 15 14 16 5 5 8 10 11 12 14 15 17 18 16 18 19 17 6 6 9 11 14 13 17 18 21 20 22 22 21 23 7 7 11 13 16 17 20 21 24 25 23 26 25 27 8 8 12 15 18 19 23 22 28 27 29 29 30 28 9 9 14 17 21 20 26 25 31 32 30 33 32 34 10 10 15 19 23 22 29 28 35 34 36 36 37 35 11 11 17 21 25 26 32 31 38 37 39 40 41 39 12 12 18 23 27 28 34 35 41 42 40 44 43 45 13 13 20 25 30 29 37 38 45 44 46 47 48 46 14 14 21 27 32 33 40 41 48 49 47 51 52 50 15 15 23 29 34 35 43 44 52 51 53 55 54 56 16 16 24 30 37 36 46 45 55 56 54 58 59 57 17 17 26 32 39 38 49 48 59 58 60 62 61 63 18 18 27 34 41 42 52 51 62 63 61 66 65 67 19 19 29 36 44 43 55 54 66 65 67 69 70 68 20 20 30 38 46 45 57 58 69 70 68 73 72 74 21 21 32 40 48 49 60 61 72 73 71 77 76 78 22 22 33 42 50 51 63 64 76 75 77 80 81 79 23 23 35 44 53 52 66 67 79 80 78 84 83 85 24 24 36 46 55 54 69 68 83 82 84 87 88 86 25 25 38 48 57 58 72 71 86 87 85 91 92 90 26 26 39 49 60 59 75 74 90 89 91 95 94 96 27 27 41 51 62 61 78 77 93 94 92 98 99 97 28 28 42 53 64 65 80 81 97 96 98 102 103 101 29 29 44 55 66 67 83 84 100 101 99 106 105 107 30 30 45 57 69 68 86 87 104 103 105 109 110 108 Gr. Idx 3RBs 12RB 15RB  1 4 5 3 6 6 5 7 4 8  2 9 8 10 7 12 11 13 10 14  3 13 14 12 15 17 18 16 19 15  4 18 17 19 16 23 24 22 25 21  5 22 23 21 24 29 28 30 27 31  6 27 26 28 25 35 34 36 33 37  7 31 32 30 33 40 41 39 42 38  8 36 35 37 34 46 47 45 48 44  9 40 41 39 42 52 51 53 50 54 10 45 44 46 43 58 57 59 56 60 11 49 50 48 51 64 63 65 62 66 12 54 53 55 52 69 70 68 71 67 13 58 59 57 60 75 76 74 77 73 14 63 62 64 61 81 80 82 79 83 15 67 68 66 69 87 86 88 85 89 16 72 71 73 70 92 93 91 94 90 17 76 77 75 78 98 99 97 100 96 18 81 80 82 79 104 103 105 102 106 19 85 86 84 87 110 109 111 108 112 20 90 89 91 88 115 116 114 117 113 21 94 95 93 96 121 122 120 123 119 22 99 98 100 97 127 128 126 129 125 23 103 104 102 105 133 132 134 131 135 24 108 107 109 106 139 138 140 137 141 25 112 113 111 114 144 145 143 146 142 26 117 116 118 115 150 151 149 152 148 27 121 122 120 123 156 155 157 154 158 28 126 125 127 124 162 161 163 160 164 29 130 131 129 132 167 168 166 169 165 30 135 134 136 133 173 174 172 175 171

TABLE 10 Groupindex based on 3RBs 16RB 18RB 20RB 1 6 7 5 8 4 7 6 8 5 9 8 7 9 6 10 2 12 13 11 14 10 14 13 15 12 16 15 16 14 17 13 3 18 19 17 20 16 20 21 19 22 18 23 24 22 25 21 4 25 24 26 23 27 27 28 26 29 25 31 30 32 29 33 5 31 30 32 29 33 34 35 33 36 32 39 38 40 37 41 6 37 36 38 35 39 41 40 42 39 43 46 47 45 48 44 7 43 44 42 45 41 48 47 49 46 50 54 53 55 52 56 8 49 50 48 51 47 54 55 53 56 52 62 61 63 60 64 9 55 56 54 57 53 61 62 60 63 59 69 70 68 71 67 10 62 61 63 60 64 68 69 67 70 66 77 78 76 79 75 11 68 67 69 66 70 75 74 76 73 77 85 84 86 83 87 12 74 73 75 72 76 82 81 83 80 84 93 92 94 91 95 13 80 81 79 82 78 88 89 87 90 86 100 101 99 102 98 14 86 87 85 88 84 95 96 94 97 93 108 107 109 106 110 15 92 93 91 94 90 102 103 101 104 100 116 115 117 114 118 16 99 98 100 97 101 109 108 110 107 111 123 124 122 125 121 17 105 104 106 103 107 116 115 117 114 118 131 132 130 133 129 18 111 110 112 109 113 123 122 124 121 125 139 138 140 137 141 19 117 118 116 119 115 129 130 128 131 127 146 147 145 148 144 20 123 124 122 125 121 136 137 135 138 134 154 155 153 156 152 21 129 130 128 131 127 143 142 144 141 145 162 161 163 160 164 22 136 135 137 134 138 150 149 151 148 152 170 169 171 168 172 23 142 141 143 140 144 157 156 158 155 159 177 178 176 179 175 24 148 147 149 146 150 163 164 162 165 161 185 186 184 187 183 25 154 155 153 156 152 170 171 169 172 168 193 192 194 191 195 26 160 161 159 162 158 177 176 178 175 179 200 201 199 202 198 27 166 167 165 168 164 184 183 185 182 186 208 209 207 210 206 28 173 172 174 171 175 191 190 192 189 193 216 215 217 214 218 29 179 178 180 177 181 197 198 196 199 195 224 223 225 222 226 30 185 184 186 183 187 204 205 203 206 202 231 232 230 233 229 Groupindex based on 3RBs 24RB 25RBs 1 9 10 8 11 7 9 10 8 11 7 2 18 19 17 20 16 19 18 20 17 21 3 27 28 26 29 25 28 29 27 30 26 4 37 36 38 35 39 38 37 39 36 40 5 46 45 47 44 48 47 48 46 49 45 6 55 54 56 53 57 57 56 58 55 59 7 64 63 65 62 66 66 67 65 68 64 8 73 74 72 75 71 76 75 77 74 78 9 82 83 81 84 80 85 86 84 87 83 10 91 92 90 93 89 95 94 96 93 97 11 100 101 99 102 98 104 103 105 102 106 12 110 109 111 108 112 113 114 112 115 111 13 119 118 120 117 121 123 122 124 121 125 14 128 127 129 126 130 132 133 131 134 130 15 137 136 138 135 139 142 141 143 140 144 16 146 147 145 148 144 151 152 150 153 149 17 155 156 154 157 153 161 160 162 159 163 18 164 165 163 166 162 170 171 169 172 168 19 173 174 172 175 171 180 179 181 178 182 20 183 182 184 181 185 189 190 188 191 187 21 192 191 193 190 194 198 199 197 200 196 22 201 200 202 199 203 208 207 209 206 210 23 210 209 211 208 212 217 218 216 219 215 24 219 220 218 221 217 227 226 228 225 229 25 228 229 227 230 226 236 237 235 238 234 26 237 238 236 239 235 246 245 247 244 248 27 246 247 245 248 244 255 256 254 257 253 28 256 255 257 254 258 265 264 266 263 267 29 265 264 266 263 267 274 275 273 276 272 30 274 273 275 272 276 284 283 285 282 286

And, in another example, the maximum number of sequences can be predetermined to 4. The following tables 11 and 12 show this case.

TABLE 11 Group- index based on 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 15RB 1 1 2 2 2 3 3 2 3 4 2 4 3 5 4 5 3 6 6 5 7 4 2 2 3 4 5 4 6 5 7 6 8 7 8 6 9 8 10 7 12 11 13 10 3 3 5 6 7 6 9 8 10 11 9 11 10 12 13 14 12 15 17 18 16 19 4 4 6 8 9 10 11 12 14 13 15 15 14 16 18 17 19 16 23 24 22 25 5 5 8 10 11 12 14 15 17 18 16 18 19 17 22 23 21 24 29 28 30 27 6 6 9 11 14 13 17 18 21 20 22 22 21 23 27 26 28 25 35 34 36 33 7 7 11 13 16 17 20 21 24 25 23 26 25 27 31 32 30 33 40 41 39 42 8 8 12 15 18 19 23 22 28 27 29 29 30 28 36 35 37 34 46 47 45 48 9 9 14 17 21 20 26 25 31 32 30 33 32 34 40 41 39 42 52 51 53 50 10 10 15 19 23 22 29 28 35 34 36 36 37 35 45 44 46 43 58 57 59 56 11 11 17 21 25 26 32 31 38 37 39 40 41 39 49 50 48 51 64 63 65 62 12 12 18 23 27 28 34 35 41 42 40 44 43 45 54 53 55 52 69 70 68 71 13 13 20 25 30 29 37 38 45 44 46 47 48 46 58 59 57 60 75 76 74 77 14 14 21 27 32 33 40 41 48 49 47 51 52 50 63 62 64 61 81 80 82 79 15 15 23 29 34 35 43 44 52 51 53 55 54 56 67 68 66 69 87 86 88 85 16 16 24 30 37 36 46 45 55 56 54 58 59 57 72 71 73 70 92 93 91 94 17 17 26 32 39 38 49 48 59 58 60 62 61 63 76 77 75 78 98 99 97 100 18 18 27 34 41 42 52 51 62 63 61 66 65 67 81 80 82 79 104 103 105 102 19 19 29 36 44 43 55 54 66 65 67 69 70 68 85 86 84 87 110 109 111 108 20 20 30 38 46 45 57 58 69 70 68 73 72 74 90 89 91 88 115 116 114 117 21 21 32 40 48 49 60 61 72 73 71 77 76 78 94 95 93 96 121 122 120 123 22 22 33 42 50 51 63 64 76 75 77 80 81 79 99 98 100 97 127 128 126 129 23 23 35 44 53 52 66 67 79 80 78 84 83 85 103 104 102 105 133 132 134 131 24 24 36 46 55 54 69 68 83 82 84 87 88 86 108 107 109 106 139 138 140 137 25 25 38 48 57 58 72 71 86 87 85 91 92 90 112 113 111 114 144 145 143 146 26 26 39 49 60 59 75 74 90 89 91 95 94 96 117 116 118 115 150 151 149 152 27 27 41 51 62 61 78 77 93 94 92 98 99 97 121 122 120 123 156 155 157 154 28 28 42 53 64 65 80 81 97 96 98 102 103 101 126 125 127 124 162 161 163 160 29 29 44 55 66 67 83 84 100 101 99 106 105 107 130 131 129 132 167 168 166 169 30 30 45 57 69 68 86 87 104 103 105 109 110 108 135 134 136 133 173 174 172 175

TABLE 12 Groupindex based on 3RBs 16RB 18RB 20RB 1 6 7 5 8 7 6 8 5 8 7 9 6 2 12 13 11 14 14 13 15 12 15 16 14 17 3 18 19 17 20 20 21 19 22 23 24 22 25 4 25 24 26 23 27 28 26 29 31 30 32 29 5 31 30 32 29 34 35 33 36 39 38 40 37 6 37 36 38 35 41 40 42 39 46 47 45 48 7 43 44 42 45 48 47 49 46 54 53 55 52 8 49 50 48 51 54 55 53 56 62 61 63 60 9 55 56 54 57 61 62 60 63 69 70 68 71 10 62 61 63 60 68 69 67 70 77 78 76 79 11 68 67 69 66 75 74 76 73 85 84 86 83 12 74 73 75 72 82 81 83 80 93 92 94 91 13 80 81 79 82 88 89 87 90 100 101 99 102 14 86 87 85 88 95 96 94 97 108 107 109 106 15 92 93 91 94 102 103 101 104 116 115 117 114 16 99 98 100 97 109 108 110 107 123 124 122 125 17 105 104 106 103 116 115 117 114 131 132 130 133 18 111 110 112 109 123 122 124 121 139 138 140 137 19 117 118 116 119 129 130 128 131 146 147 145 148 20 123 124 122 125 136 137 135 138 154 155 153 156 21 129 130 128 131 143 142 144 141 162 161 163 160 22 136 135 137 134 150 149 151 148 170 169 171 168 23 142 141 143 140 157 156 158 155 177 178 176 179 24 148 147 149 146 163 164 162 165 185 186 184 187 25 154 155 153 156 170 171 169 172 193 192 194 191 26 160 161 159 162 177 176 178 175 200 201 199 202 27 166 167 165 168 184 183 185 182 208 209 207 210 28 173 172 174 171 191 190 192 189 216 215 217 214 29 179 178 180 177 197 198 196 199 224 223 225 222 30 185 184 186 183 204 205 203 206 231 232 230 233 Groupindex based on 3RBs 24RB 25RBs  1 9 10 8 11 9 10 8 11  2 18 19 17 20 19 18 20 17  3 27 28 26 29 28 29 27 30  4 37 36 38 35 38 37 39 36  5 46 45 47 44 47 48 46 49  6 55 54 56 53 57 56 58 55  7 64 63 65 62 66 67 65 68  8 73 74 72 75 76 75 77 74  9 82 83 81 84 85 86 84 87 10 91 92 90 93 95 94 96 93 11 100 101 99 102 104 103 105 102 12 110 109 111 108 113 114 112 115 13 119 118 120 117 123 122 124 121 14 128 127 129 126 132 133 131 134 15 137 136 138 135 142 141 143 140 16 146 147 145 148 151 152 150 153 17 155 156 154 157 161 160 162 159 18 164 165 163 166 170 171 169 172 19 173 174 172 175 180 179 181 178 20 183 182 184 181 189 190 188 191 21 192 191 193 190 198 199 197 200 22 201 200 202 199 208 207 209 206 23 210 209 211 208 217 218 216 219 24 219 220 218 221 227 226 228 225 25 228 229 227 230 236 237 235 238 26 237 238 236 239 246 245 247 244 27 246 247 245 248 255 256 254 257 28 256 255 257 254 265 264 266 263 29 265 264 266 263 274 275 273 276 30 274 273 275 272 284 283 285 282

And, in another example, the maximum number of sequences can be predetermined to 3. The following tables 13 and 14 show this case.

TABLE 13 Groupindex based on 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 1 1 2 2 2 3 3 2 3 4 2 4 3 5 4 5 3 2 2 3 4 5 4 6 5 7 6 8 7 8 6 9 8 10 3 3 5 6 7 6 9 8 10 11 9 11 10 12 13 14 12 4 4 6 8 9 10 11 12 14 13 15 15 14 16 18 17 19 5 5 8 10 11 12 14 15 17 18 16 18 19 17 22 23 21 6 6 9 11 14 13 17 18 21 20 22 22 21 23 27 26 28 7 7 11 13 16 17 20 21 24 25 23 26 25 27 31 32 30 8 8 12 15 18 19 23 22 28 27 29 29 30 28 36 35 37 9 9 14 17 21 20 26 25 31 32 30 33 32 34 40 41 39 10 10 15 19 23 22 29 28 35 34 36 36 37 35 45 44 46 11 11 17 21 25 26 32 31 38 37 39 40 41 39 49 50 48 12 12 18 23 27 28 34 35 41 42 40 44 43 45 54 53 55 13 13 20 25 30 29 37 38 45 44 46 47 48 46 58 59 57 14 14 21 27 32 33 40 41 48 49 47 51 52 50 63 62 64 15 15 23 29 34 35 43 44 52 51 53 55 54 56 67 68 66 16 16 24 30 37 36 46 45 55 56 54 58 59 57 72 71 73 17 17 26 32 39 38 49 48 59 58 60 62 61 63 76 77 75 18 18 27 34 41 42 52 51 62 63 61 66 65 67 81 80 82 19 19 29 36 44 43 55 54 66 65 67 69 70 68 85 86 84 20 20 30 38 46 45 57 58 69 70 68 73 72 74 90 89 91 21 21 32 40 48 49 60 61 72 73 71 77 76 78 94 95 93 22 22 33 42 50 51 63 64 76 75 77 80 81 79 99 98 100 23 23 35 44 53 52 66 67 79 80 78 84 83 85 103 104 102 24 24 36 46 55 54 69 68 83 82 84 87 88 86 108 107 109 25 25 38 48 57 58 72 71 86 87 85 91 92 90 112 113 111 26 26 39 49 60 59 75 74 90 89 91 95 94 96 117 116 118 27 27 41 51 62 61 78 77 93 94 92 98 99 97 121 122 120 28 28 42 53 64 65 80 81 97 96 98 102 103 101 126 125 127 29 29 44 55 66 67 83 84 100 101 99 106 105 107 130 131 129 30 30 45 57 69 68 86 87 104 103 105 109 110 108 135 134 136 Groupindex based on 3RBs 15RB 16RB 18RB  1 6 5 7 6 7 5 7 6 8  2 12 11 13 12 13 11 14 13 15  3 17 18 16 18 19 17 20 21 19  4 23 24 22 25 24 26 27 28 26  5 29 28 30 31 30 32 34 35 33  6 35 34 36 37 36 38 41 40 42  7 40 41 39 43 44 42 48 47 49  8 46 47 45 49 50 48 54 55 53  9 52 51 53 55 56 54 61 62 60 10 58 57 59 62 61 63 68 69 67 11 64 63 65 68 67 69 75 74 76 12 69 70 68 74 73 75 82 81 83 13 75 76 74 80 81 79 88 89 87 14 81 80 82 86 87 85 95 96 94 15 87 86 88 92 93 91 102 103 101 16 92 93 91 99 98 100 109 108 110 17 98 99 97 105 104 106 116 115 117 18 104 103 105 111 110 112 123 122 124 19 110 109 111 117 118 116 129 130 128 20 115 116 114 123 124 122 136 137 135 21 121 122 120 129 130 128 143 142 144 22 127 128 126 136 135 137 150 149 151 23 133 132 134 142 141 143 157 156 158 24 139 138 140 148 147 149 163 164 162 25 144 145 143 154 155 153 170 171 169 26 150 151 149 160 161 159 177 176 178 27 156 155 157 166 167 165 184 183 185 28 162 161 163 173 172 174 191 190 192 29 167 168 166 179 178 180 197 198 196 30 173 174 172 185 184 186 204 205 203

TABLE 14 Group- index based on 3RBs 20RB 24RB 25RBs 1 8 7 9 9 10 8 9 10 8 2 15 16 14 18 19 17 19 18 20 3 23 24 22 27 28 26 28 29 27 4 31 30 32 37 36 38 38 37 39 5 39 38 40 46 45 47 47 48 46 6 46 47 45 55 54 56 57 56 58 7 54 53 55 64 63 65 66 67 65 8 62 61 63 73 74 72 76 75 77 9 69 70 68 82 83 81 85 86 84 10 77 78 76 91 92 90 95 94 96 11 85 84 86 100 101 99 104 103 105 12 93 92 94 110 109 111 113 114 112 13 100 101 99 119 118 120 123 122 124 14 108 107 109 128 127 129 132 133 131 15 116 115 117 137 136 138 142 141 143 16 123 124 122 146 147 145 151 152 150 17 131 132 130 155 156 154 161 160 162 18 139 138 140 164 165 163 170 171 169 19 146 147 145 173 174 172 180 179 181 20 154 155 153 183 182 184 189 190 188 21 162 161 163 192 191 193 198 199 197 22 170 169 171 201 200 202 208 207 209 23 177 178 176 210 209 211 217 218 216 24 185 186 184 219 220 218 227 226 228 25 193 192 194 228 229 227 236 237 235 26 200 201 199 237 238 236 246 245 247 27 208 209 207 246 247 245 255 256 254 28 216 215 217 256 255 257 265 264 266 29 224 223 225 265 264 266 274 275 273 30 231 232 230 274 273 275 284 283 285

And, in another example, the maximum number of sequences can be predetermined to 2. The following tables 15 and 16 show this case.

TABLE 15 Groupindex based on 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 15RB 1 1 2 2 2 3 3 2 3 4 4 3 4 5 6 5 2 2 3 4 5 4 6 5 7 6 7 8 9 8 12 11 3 3 5 6 7 6 9 8 10 11 11 10 13 14 17 18 4 4 6 8 9 10 11 12 14 13 15 14 18 17 23 24 5 5 8 10 11 12 14 15 17 18 18 19 22 23 29 28 6 6 9 11 14 13 17 18 21 20 22 21 27 26 35 34 7 7 11 13 16 17 20 21 24 25 26 25 31 32 40 41 8 8 12 15 18 19 23 22 28 27 29 30 36 35 46 47 9 9 14 17 21 20 26 25 31 32 33 32 40 41 52 51 10 10 15 19 23 22 29 28 35 34 36 37 45 44 58 57 11 11 17 21 25 26 32 31 38 37 40 41 49 50 64 63 12 12 18 23 27 28 34 35 41 42 44 43 54 53 69 70 13 13 20 25 30 29 37 38 45 44 47 48 58 59 75 76 14 14 21 27 32 33 40 41 48 49 51 52 63 62 81 80 15 15 23 29 34 35 43 44 52 51 55 54 67 68 87 86 16 16 24 30 37 36 46 45 55 56 58 49 72 71 92 93 17 17 26 32 39 38 49 48 59 58 62 61 76 77 98 99 18 18 27 34 41 42 52 51 62 63 66 65 81 80 104 103 19 19 29 36 44 43 55 54 66 65 69 70 85 86 110 109 20 20 30 38 46 45 57 58 69 70 73 72 90 89 115 116 21 21 32 40 48 49 60 61 72 73 77 76 94 95 121 122 22 22 33 42 50 51 63 64 76 75 80 81 99 98 127 128 23 23 35 44 53 52 66 67 79 80 84 83 103 104 133 132 24 24 36 46 55 54 69 68 83 82 87 88 108 107 139 138 25 25 38 48 57 58 72 71 86 87 91 92 112 113 144 145 26 26 39 49 60 59 75 74 90 89 95 94 117 116 150 151 27 27 41 51 62 61 78 77 93 94 98 99 121 122 156 155 28 28 42 53 64 65 80 81 97 96 102 103 126 125 162 161 29 29 44 55 66 67 83 84 100 101 106 105 130 131 167 168 30 30 45 57 69 68 86 87 104 103 109 110 135 134 173 174

TABLE 16 Gr. Idx 3RBs 16RB 18RB 20RB 24RB 25RB 1 6 7 7 6 8 7 9 10 9 10 2 12 13 14 13 15 16 18 19 19 18 3 18 19 20 21 23 24 27 28 28 29 4 25 24 27 28 31 30 37 36 38 37 5 31 30 34 35 39 38 46 45 47 48 6 37 36 41 40 46 47 55 54 57 56 7 43 44 48 47 54 53 64 63 66 67 8 49 50 54 55 62 61 73 74 76 75 9 55 56 61 62 69 70 82 83 85 86 10 62 61 68 69 77 78 91 92 95 94 11 68 67 75 74 85 84 100 101 104 103 12 74 73 82 81 93 92 110 109 113 114 13 80 81 88 89 100 101 119 118 123 122 14 86 87 95 96 108 107 128 127 132 133 15 92 93 102 103 116 115 137 136 142 141 16 99 98 109 108 123 124 146 147 151 152 17 105 104 116 115 131 132 155 156 161 160 18 111 110 123 122 139 138 164 165 170 171 19 117 118 129 130 146 147 173 174 180 179 20 123 124 136 137 154 155 183 182 189 190 21 129 130 143 142 162 161 192 191 198 199 22 136 135 150 149 170 169 201 200 208 207 23 142 141 157 156 177 178 210 209 217 218 24 148 147 163 164 185 186 219 220 227 226 25 154 155 170 171 193 192 228 229 236 237 26 160 161 177 176 200 201 237 238 246 245 27 166 167 184 183 208 209 246 247 255 256 28 173 172 191 190 216 215 256 255 265 264 29 179 178 197 198 224 223 265 264 274 275 30 185 184 204 205 231 232 274 273 284 283

And, in another example, the maximum number of sequences can be predetermined to 1. The following table 17 shows this case.

TABLE 17 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 15RB 16RB 18RB 20RB 24RB 25RB 1 1 2 2 2 3 3 4 4 6 6 7 8 9 9 2 2 3 4 5 6 7 7 9 12 12 14 15 18 19 3 3 5 6 7 9 10 11 13 17 18 20 23 27 28 4 4 6 8 9 11 14 15 18 23 25 27 31 37 38 5 5 8 10 11 14 17 18 22 29 31 34 39 46 47 6 6 9 11 14 17 21 22 27 35 37 41 46 55 57 7 7 11 13 16 20 24 26 31 40 43 48 54 64 66 8 8 12 15 18 23 28 29 36 46 49 54 62 73 76 9 9 14 17 21 26 31 33 40 52 55 61 69 82 85 10 10 15 19 23 29 35 36 45 58 62 68 77 91 95 11 11 17 21 25 32 38 40 49 64 68 75 85 100 104 12 12 18 23 27 34 41 44 54 69 74 82 93 110 113 13 13 20 25 30 37 45 47 58 75 80 88 100 119 123 14 14 21 27 32 40 48 51 63 81 86 95 108 128 132 15 15 23 29 34 43 52 55 67 87 92 102 116 137 142 16 16 24 30 37 46 55 58 72 92 99 109 123 146 151 17 17 26 32 39 49 59 62 76 98 105 116 131 155 161 18 18 27 34 41 52 62 66 81 104 111 123 139 164 170 19 19 29 36 44 55 66 69 85 110 117 129 146 173 180 20 20 30 38 46 57 69 73 90 115 123 136 154 183 189 21 21 32 40 48 60 72 77 94 121 129 143 162 192 198 22 22 33 42 50 63 76 80 99 127 136 150 170 201 208 23 23 35 44 53 66 79 84 103 133 142 157 177 210 217 24 24 36 46 55 69 83 87 108 139 148 163 185 219 227 25 25 38 48 57 72 86 91 112 144 154 170 193 228 236 26 26 39 49 60 75 90 95 117 150 160 177 200 237 246 27 27 41 51 62 78 93 98 121 156 166 184 208 246 255 28 28 42 53 64 80 97 102 126 162 173 191 216 256 265 29 29 44 55 66 83 100 106 130 167 179 197 224 265 274 30 30 45 57 69 86 104 109 135 173 185 204 231 274 284

Considering the complexity of configuration and the flexibility for supporting UE(s) to use variable length reference signal sequence, one embodiment of this invention proposes to perform grouping such that each of the groups contains one base sequence of each length corresponding to 1 to 5 RB length, and two base sequences of each length corresponding to 6 RB or more length. This corresponds to the tables 15 and 16.

Here, base sequence means the ZC sequence indicated by the root index, and is used for applying the cyclic shift corresponding to various cyclic shift values. And, the base sequence with cyclic shift can be used as a reference signal sequence.

The above tables 1˜17 is the case when the root index(es) is selected by using the term of (s₁/N₁−s₂/N₂). But in another embodiment of this invention, the root index(es) can be selected by actual cross correlation value calculation. The following tables 18˜20 correspond to the tables 6˜8, but the root indexes are selected by actual cross correlation value calculation.

TABLE 18 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 1 1 25 2 20 2 3 25 57 4 75 60 79 4 2 2 3 4 40 33 65 28 7 71 96 64 45 75 3 3 14 6 7 21 53 9 46 10 37 11 39 86 4 4 6 47 9 66 56 41 14 85 78 15 71 14 5 5 39 39 47 54 44 50 71 44 60 56 75 103 6 6 9 31 61 14 17 84 21 92 85 97 50 67 7 7 42 33 16 28 20 87 24 51 60 82 63 26 8 8 12 30 42 54 23 5 28 99 49 67 86 1 9 9 45 17 68 21 48 85 31 74 58 61 89 78 10 10 15 19 23 5 73 29 106 70 34 93 112 36 11 11 1 21 11 25 32 2 38 102 11 40 78 12 12 12 37 23 51 63 79 64 96 77 41 72 44 100 13 13 4 5 6 30 67 37 45 9 18 104 47 85 14 14 21 7 32 22 40 58 102 84 48 51 6 23 15 15 23 58 58 34 43 61 105 16 25 17 111 83 16 16 24 1 13 65 46 28 91 2 82 96 2 30 17 17 26 52 39 49 31 49 23 59 16 62 107 90 18 18 43 54 65 41 22 52 62 98 89 9 66 28 19 19 29 36 8 20 10 25 30 12 87 41 24 70 20 20 46 38 46 60 87 57 69 5 96 73 35 101 21 21 32 40 48 66 16 60 1 37 73 20 1 39 22 22 2 42 3 50 41 78 76 49 33 52 24 35 23 23 35 29 29 17 66 55 79 8 58 46 27 112 24 24 5 26 55 43 69 2 83 56 47 31 12 88 25 25 38 28 10 57 72 27 15 65 86 63 46 16 26 26 8 20 24 17 45 75 63 54 90 95 57 38 27 27 41 22 62 44 33 48 93 22 29 23 98 42 28 28 33 53 64 50 36 80 61 97 70 102 57 74 29 29 44 8 31 38 24 39 100 36 11 49 68 106 30 30 22 55 69 51 86 64 50 103 18 34 109 81 Gr. Idx 3RBs 12RB 15RB  1 74 51 4 5 6 95 140 125 5  2 9 120 44 8 101 71 131 12 11  3 83 13 14 48 17 107 77 18 62  4 18 122 87 129 23 83 113 68 24  5 92 23 115 78 29 118 148 28 163  6 27 96 131 73 35 154 124 34 94  7 101 124 32 66 40 130 160 41 100  8 36 105 8 59 46 136 106 47 91  9 133 110 41 75 52 141 171 142 7 10 45 114 91 17 58 147 57 177 13 11 119 3 50 77 64 153 4 63 19 12 54 100 123 26 69 159 129 114 10 13 12 58 128 114 75 165 153 120 76 14 63 132 7 35 81 21 170 36 80 15 67 137 21 68 86 27 176 146 42 16 2 118 71 16 93 152 3 33 137 17 7 76 77 132 158 98 9 143 134 18 11 127 81 25 104 14 44 59 103 19 85 39 16 113 20 50 110 65 169 20 136 20 89 43 115 26 175 116 71 21 94 48 25 129 121 32 122 2 166 22 6 64 52 99 127 38 8 172 67 23 103 34 131 80 133 73 132 88 43 24 38 15 73 108 139 49 19 138 79 25 112 66 43 113 144 25 55 145 85 26 47 116 24 61 150 61 31 151 16 27 121 75 52 17 156 96 155 66 111 28 56 79 126 125 162 72 102 42 161 29 130 95 19 131 78 48 108 167 168 30 65 135 134 100 173 54 84 39 174

TABLE 19 Gr. Idx 3RBs 16RB 18RB 20RB 1 6 102 70 54 7 159 112 7 6 165 49 147 8 8 7 167 127 87 9 187 2 76 12 108 140 60 13 119 14 84 154 98 56 13 15 135 95 175 75 16 111 3 18 114 19 82 66 146 20 126 91 161 21 73 147 23 143 103 24 142 22 71 4 25 152 120 24 88 168 133 28 168 98 196 80 154 31 150 190 30 32 210 111 5 30 158 174 69 31 107 34 175 139 33 35 87 203 39 38 158 118 218 198 98 6 37 132 101 133 180 38 41 146 40 199 182 181 83 46 126 47 45 106 94 206 7 43 139 107 91 44 170 48 153 118 188 206 47 174 54 174 173 134 53 55 213 8 49 113 145 50 97 177 54 195 139 181 2 55 53 62 181 221 61 2 141 63 9 151 103 56 132 183 8 61 202 62 132 114 19 167 69 189 70 149 129 229 10 10 62 157 189 61 14 125 68 174 209 173 138 121 69 77 197 157 196 76 236 137 11 68 67 163 20 106 4 75 74 76 5 181 180 159 85 204 5 84 164 25 86 12 74 169 10 138 170 75 187 152 81 82 166 29 208 92 13 172 33 152 236 212 13 80 176 81 144 79 16 194 36 141 159 18 89 173 220 180 101 21 100 160 148 14 86 150 182 87 10 48 95 201 25 96 11 166 180 108 107 109 188 228 48 168 15 188 93 29 156 92 140 102 208 32 103 172 101 207 116 36 235 115 195 56 68 16 3 98 162 35 99 51 109 3 179 56 110 39 4 123 203 4 124 44 183 171 17 105 41 9 104 181 143 116 10 186 115 200 31 45 131 132 130 51 11 191 71 18 111 47 15 110 175 149 17 175 70 52 193 122 38 19 59 138 139 218 140 79 19 117 22 181 21 116 53 24 59 130 182 129 45 3 27 147 146 226 206 87 67 20 28 123 124 171 85 187 136 31 137 135 206 52 66 35 154 234 155 214 75 153 21 129 34 2 66 130 177 143 37 2 73 142 196 185 162 42 82 43 163 3 102 22 135 136 59 8 183 21 150 9 149 44 79 97 192 170 169 50 90 110 10 74 23 142 78 46 94 141 14 16 30 209 157 72 156 158 58 177 18 178 237 98 176 24 148 52 84 100 147 21 163 93 23 5 58 164 111 185 65 66 105 186 184 26 25 154 59 90 155 58 11 170 65 171 12 64 128 86 193 113 192 33 194 133 97 26 33 161 17 122 160 84 177 72 176 178 36 8 71 200 81 121 41 21 201 141 27 166 39 71 167 103 23 78 183 43 113 15 131 185 208 89 49 209 207 29 128 28 173 77 45 172 109 125 85 50 138 190 191 64 32 216 96 97 215 217 136 56 29 115 179 51 131 178 83 92 197 127 57 113 155 198 224 223 104 144 64 164 128 30 185 89 121 137 184 70 46 99 204 205 162 64 98 232 231 72 112 152 230 52

TABLE 20 Gr. Idx 3RBs 24RB 25RB 1 9 151 150 103 80 198 10 8 221 9 10 156 107 205 229 8 68 83 2 19 207 18 17 159 89 188 75 231 19 165 18 214 92 166 20 239 136 3 28 27 169 216 122 240 26 98 84 28 175 126 27 248 29 224 102 87 4 36 37 178 225 35 131 93 249 263 38 184 135 39 136 233 37 111 155 5 140 45 234 46 187 47 272 188 258 194 48 145 47 243 193 267 242 106 6 55 196 149 197 243 56 267 54 244 56 203 252 154 130 58 155 174 57 7 65 205 158 206 253 63 65 252 135 66 213 212 164 262 261 67 286 139 8 73 214 262 74 72 168 144 215 243 76 222 75 271 173 149 77 2 17 9 82 223 81 271 177 83 176 153 224 85 231 183 12 86 280 84 281 158 10 91 280 92 90 186 232 233 21 185 95 241 192 94 168 96 21 290 93 11 242 195 6 101 99 100 30 44 102 104 250 251 6 202 103 105 31 201 12 109 110 204 39 15 251 111 180 166 113 260 211 16 112 40 114 115 187 13 119 213 260 24 120 48 118 261 232 123 269 25 270 221 196 220 122 124 14 128 33 270 34 222 269 127 129 71 132 230 133 131 279 278 34 191 35 15 137 136 138 278 66 43 231 42 208 288 142 44 239 289 240 143 83 259 16 146 147 4 145 5 217 240 52 75 5 151 249 54 4 53 34 210 150 17 155 13 249 61 14 156 154 250 212 161 63 160 162 15 14 102 259 258 18 164 70 23 259 163 165 22 51 108 170 24 268 23 72 97 73 171 169 19 174 173 32 79 172 244 268 103 117 180 33 179 82 277 181 253 178 106 20 41 183 277 182 88 184 253 239 181 189 43 42 287 91 190 188 262 92 21 192 50 3 191 193 97 262 135 98 198 52 101 199 125 200 197 3 272 22 201 60 202 12 106 59 200 107 130 208 62 110 281 207 13 209 12 135 23 210 69 21 209 211 139 68 40 97 218 71 22 120 217 144 216 291 276 24 219 78 125 77 30 220 31 218 148 227 80 81 129 228 31 32 226 7 25 87 228 134 86 40 227 39 229 16 237 90 41 139 163 235 138 236 119 26 96 143 49 237 25 238 236 11 124 99 245 148 246 50 247 100 26 51 27 247 246 105 58 248 152 190 34 20 255 109 254 158 157 60 256 182 108 28 256 114 67 161 255 185 257 43 199 265 118 167 266 45 264 69 119 191 29 264 76 265 123 266 194 124 95 208 274 128 275 127 79 273 201 157 54 30 274 132 180 85 273 275 133 104 62 284 283 137 186 88 64 282 285 210

In this case, if the maximum number of sequences per each group is predetermined to 5, the grouping can be performed as shown in the following tables 21 and 22. The tables 21 and 22 are also the case when the base sequences are selected by actual cross correlation calculation.

TABLE 21 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 1 1 25 2 20 2 3 25 57 4 75 60 79 4 2 2 3 4 40 33 65 28 7 71 96 64 45 75 3 3 14 6 7 21 53 9 46 10 37 11 39 86 4 4 6 47 9 66 56 41 14 85 78 15 71 14 5 5 39 39 47 54 44 50 71 44 60 56 75 103 6 6 9 31 61 14 17 84 21 92 85 97 50 67 7 7 42 33 16 28 20 87 24 51 60 82 63 26 8 8 12 30 42 54 23 5 28 99 49 67 86 1 9 9 45 17 68 21 48 85 31 74 58 61 89 78 10 10 15 19 23 5 73 29 106 70 34 93 112 36 11 11 1 21 11 25 32 2 38 102 11 40 78 12 12 12 37 23 51 63 79 64 95 77 41 72 44 100 13 13 4 5 6 30 67 37 45 9 18 104 47 85 14 14 21 7 32 22 40 58 102 84 48 51 6 23 15 15 23 58 58 34 43 61 105 16 25 17 111 83 16 16 24 1 13 65 46 28 91 2 82 96 2 30 17 17 26 52 39 49 31 49 23 59 16 62 107 90 18 18 43 54 65 41 22 52 62 98 89 9 66 28 19 19 29 36 8 20 10 25 30 12 87 41 24 70 20 20 46 38 46 60 87 57 69 5 96 73 35 101 21 21 32 40 48 66 16 60 1 37 73 20 1 39 22 22 2 42 3 50 41 78 76 49 33 52 24 35 23 23 35 29 29 17 66 55 79 8 58 46 27 112 24 24 5 26 55 43 69 2 83 56 47 31 12 88 25 25 38 28 10 57 72 27 15 65 86 63 46 16 26 26 8 20 24 17 45 75 63 54 90 95 57 38 27 27 41 22 62 44 33 48 93 22 29 23 98 42 28 28 33 53 64 50 36 80 61 97 70 102 57 74 29 29 44 8 31 38 24 39 100 39 11 49 68 106 30 30 22 55 69 51 86 64 50 103 18 34 109 81 Gr. Idx 3RBs 12RB 15RB  1 74 51 4 5 6 95 140 125 5  2 9 120 44 8 101 71 131 12 11  3 83 13 14 48 17 107 77 18 62  4 18 122 87 129 23 83 113 68 24  5 92 23 115 78 29 118 148 28 163  6 27 96 131 73 35 154 124 34 94  7 101 124 32 66 40 130 160 41 100  8 36 105 8 59 46 136 106 47 91  9 133 110 41 75 52 141 171 142 7 10 45 114 91 17 58 147 57 177 13 11 119 3 50 77 64 153 4 63 19 12 54 100 123 26 69 159 129 114 10 13 12 58 128 114 75 165 135 120 76 14 63 132 7 35 81 21 170 36 80 15 67 137 21 68 86 27 176 146 42 16 2 118 71 16 93 152 3 33 137 17 7 76 77 132 158 98 9 143 134 18 11 127 81 25 104 14 44 59 103 19 85 39 16 113 20 50 110 65 169 20 136 20 89 43 115 26 175 116 71 21 94 48 25 129 121 32 122 2 166 22 6 64 52 99 127 38 8 172 67 23 103 34 131 80 133 73 132 88 43 24 38 15 73 108 139 49 19 138 79 25 112 66 43 113 144 25 55 145 85 26 47 116 24 61 150 61 31 151 16 27 121 75 52 17 156 96 155 66 111 28 56 79 126 125 162 72 102 42 161 29 130 95 19 131 78 48 108 167 168 30 65 135 134 100 173 54 84 39 174

TABLE 22 Gr. Idx 3RBs 16RB 18RB 20RB 1 6 102 70 54 7 112 7 6 165 49 8 7 167 127 87 2 76 12 108 140 60 119 14 84 154 98 15 135 95 175 75 3 18 114 19 82 66 20 126 91 161 21 23 143 103 24 142 4 25 152 120 24 88 133 28 168 98 196 31 150 190 30 32 5 30 158 174 69 31 34 175 139 33 35 39 38 158 118 218 6 37 132 101 133 180 41 146 40 199 182 46 126 47 45 106 7 43 139 107 91 44 48 153 118 188 206 54 174 173 134 53 8 49 113 145 50 97 54 195 139 181 2 62 181 221 61 2 9 151 103 56 132 183 61 202 62 132 114 69 189 70 149 129 10 62 157 189 61 14 68 174 209 173 138 77 197 157 196 76 11 68 67 163 20 106 75 74 76 5 181 85 204 5 84 164 12 74 169 10 138 170 187 152 81 82 166 92 13 172 33 152 13 80 176 81 144 79 194 36 141 159 18 220 180 101 21 100 14 86 150 182 87 10 95 201 25 96 11 108 107 109 188 228 15 188 93 29 156 92 102 208 32 103 172 116 36 235 115 195 16 3 98 162 35 99 109 3 179 56 110 123 203 4 124 44 17 105 41 9 104 181 116 10 186 115 200 131 132 130 51 11 18 111 47 15 110 175 17 175 70 52 193 19 59 138 139 218 19 117 22 181 21 116 24 59 130 182 129 27 147 146 226 206 20 28 123 124 171 85 136 31 137 135 206 35 154 234 155 214 21 129 34 2 66 130 143 37 2 73 142 162 42 82 43 163 22 135 136 59 8 183 150 9 149 44 79 170 169 50 90 110 23 142 78 46 94 141 16 30 209 157 72 58 177 18 178 237 24 148 52 84 100 147 163 93 23 5 58 185 65 66 105 186 25 154 59 90 155 58 170 65 171 12 64 193 113 192 33 194 26 33 161 17 122 160 177 72 176 178 36 200 81 121 41 21 27 166 39 71 167 103 78 183 43 113 15 208 89 49 209 207 28 173 77 45 172 109 85 50 138 190 191 216 96 97 215 217 29 115 179 51 131 178 92 197 127 57 113 224 223 104 144 64 30 185 89 121 137 184 46 99 204 205 162 232 231 72 112 152 Gr. Idx 3RBs 24RB 25RBs  1 9 151 150 103 80 9 10 156 107 205  2 19 207 18 17 159 19 165 18 214 92  3 28 27 169 216 122 28 175 126 27 248  4 36 37 178 225 35 38 184 135 39 136  5 140 45 234 46 187 194 48 145 47 243  6 55 196 149 197 243 56 203 252 154 130  7 64 205 158 206 253 66 213 212 164 262  8 73 214 262 74 72 76 222 75 271 173  9 82 223 81 271 177 85 231 183 12 86 10 91 280 92 90 186 95 241 192 94 168 11 242 195 6 101 99 104 250 251 6 202 12 109 110 204 39 15 113 260 211 16 112 13 119 213 260 24 120 123 269 25 270 221 14 128 33 270 34 222 132 230 133 131 279 15 137 136 138 278 66 288 142 44 239 289 16 146 147 4 145 5 5 151 249 54 4 17 155 13 249 61 14 161 63 160 162 15 18 164 70 23 259 163 170 24 268 23 72 19 174 173 32 79 172 180 33 179 82 277 20 41 183 277 182 88 189 43 42 287 91 21 192 50 3 191 193 198 52 101 199 125 22 201 60 202 12 106 208 62 110 281 207 23 210 69 21 209 211 218 71 22 120 217 24 219 78 125 77 30 227 80 81 129 228 25 87 228 134 86 40 237 90 41 139 163 26 96 143 49 237 25 99 245 148 246 50 27 247 246 105 58 248 255 109 254 158 157 28 256 114 67 161 255 265 118 167 266 45 29 264 76 265 123 266 274 128 275 127 79 30 274 132 180 85 273 284 283 137 186 88

In another example, if the maximum number of sequences per each group is predetermined to 4, the grouping can be performed as shown in the following tables 23 and 24. The tables 23 and 24 are also the case when the base sequences are selected by actual cross correlation calculation.

TABLE 23 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 15RB 1 1 25 2 20 2 3 25 57 4 75 60 79 4 74 51 4 5 6 95 140 125 2 2 3 4 40 33 65 28 7 71 96 64 45 75 9 120 44 8 101 71 131 12 3 3 14 6 7 21 53 9 46 10 37 11 39 86 83 13 14 48 17 107 77 18 4 4 6 47 9 66 56 41 14 85 78 15 71 14 18 122 87 129 23 83 113 68 5 5 39 39 47 54 44 50 71 44 60 56 75 103 92 23 115 78 29 118 148 28 6 6 9 31 61 14 17 84 21 92 85 97 50 67 27 96 131 73 35 154 124 34 7 7 42 33 16 28 20 87 24 51 60 82 63 26 101 124 32 66 40 130 160 41 8 8 12 30 42 54 23 5 28 99 49 67 86 1 36 105 8 59 46 136 106 47 9 9 45 17 68 21 48 85 31 74 58 61 89 78 133 110 41 75 52 141 171 142 10 10 15 19 23 5 73 29 106 70 34 93 112 36 45 114 91 17 58 147 57 177 11 11 1 21 11 25 32 2 38 102 11 40 78 12 119 3 50 77 64 153 4 63 12 12 37 23 51 63 79 64 95 77 41 72 44 100 54 100 123 26 69 159 129 114 13 13 4 5 6 30 67 37 45 9 18 104 47 85 12 58 128 114 75 165 135 120 14 14 21 7 32 22 40 58 102 84 48 51 6 23 63 132 7 35 81 21 170 36 15 15 23 58 58 34 43 61 105 16 25 17 111 83 67 137 21 68 86 27 176 146 16 16 24 1 13 65 46 28 91 2 82 96 2 30 2 118 71 16 93 152 3 33 17 17 26 52 39 49 31 49 23 59 16 62 107 90 7 76 77 132 158 98 9 143 18 18 43 54 65 41 22 52 62 98 89 9 66 28 11 127 81 25 104 14 44 59 19 19 29 36 8 20 10 25 30 12 87 41 24 70 85 39 16 113 20 50 110 65 20 20 46 38 46 60 87 57 69 5 96 73 35 101 136 20 89 43 115 26 175 116 21 21 32 40 48 66 16 60 1 37 73 20 1 39 94 48 25 129 121 32 122 2 22 22 2 42 3 50 41 78 76 49 33 52 24 35 6 64 52 99 127 38 8 172 23 23 35 29 29 17 66 55 79 8 58 46 27 112 103 34 131 80 133 73 132 88 24 24 5 26 55 43 69 2 83 56 47 31 12 88 38 15 73 108 139 49 19 138 25 25 38 28 10 57 72 27 15 65 86 63 46 16 112 66 43 113 144 25 55 145 26 26 8 20 24 17 45 75 63 54 90 95 57 38 47 116 24 61 150 61 31 151 27 27 41 22 62 44 33 48 93 22 29 23 98 42 121 75 52 17 156 96 155 66 28 28 33 53 64 50 36 80 61 97 70 102 57 74 56 79 126 125 162 72 102 42 29 29 44 8 31 38 24 39 100 36 11 49 68 106 130 95 19 131 78 48 180 167 30 30 22 55 69 51 86 64 50 103 18 34 109 81 65 135 134 100 173 54 84 39

TABLE 24 Gr. Idx 3RBs 3RB 18RB 20RB 24RB 25RBs 1 6 102 70 54 112 7 6 165 8 7 167 127 9 151 150 103 9 10 156 107 2 76 12 108 140 119 14 84 154 15 135 95 175 19 207 18 17 19 165 18 214 3 18 114 19 82 20 126 91 161 23 143 103 24 28 27 169 216 28 175 126 27 4 25 152 120 24 133 28 168 98 31 150 190 30 36 37 178 225 38 184 135 39 5 30 158 174 69 34 175 139 33 39 38 158 118 140 45 234 46 194 48 145 47 6 37 132 101 133 41 146 40 199 46 126 47 45 55 196 149 197 56 203 252 154 7 43 139 107 91 48 153 118 188 54 174 173 134 64 205 158 206 66 213 212 164 8 49 113 145 50 54 195 139 181 62 181 221 61 73 214 262 74 76 222 75 271 9 151 103 56 132 61 202 62 132 69 189 70 149 82 223 81 271 85 231 183 12 10 62 157 189 61 68 174 209 173 77 197 157 196 91 280 92 90 95 241 192 94 11 68 67 163 20 75 74 76 5 85 204 5 84 242 195 6 101 104 250 251 6 12 74 169 10 138 187 152 81 82 92 13 172 33 109 110 204 39 113 260 211 16 13 80 176 81 144 194 36 141 159 220 180 101 21 119 213 260 24 123 269 25 270 14 86 150 182 87 95 201 25 96 108 107 109 188 128 33 270 34 132 230 133 131 15 188 93 29 156 102 208 32 103 116 36 235 115 137 136 138 278 288 142 44 239 16 3 98 162 35 109 3 179 56 123 203 4 124 146 147 4 145 5 151 249 54 17 105 41 9 104 116 10 186 115 131 132 130 51 155 13 249 61 161 63 160 162 18 111 47 15 110 17 175 70 52 19 59 138 139 164 70 23 259 170 24 268 23 19 117 22 181 21 24 59 130 182 27 147 146 226 174 173 32 79 180 33 179 82 20 28 123 124 171 136 31 137 135 35 154 234 155 41 183 277 182 189 43 42 287 21 129 34 2 66 143 37 2 73 162 42 82 43 192 50 3 191 198 52 101 199 22 135 136 59 8 150 9 149 44 170 169 50 90 201 60 202 12 208 62 110 281 23 142 78 46 94 16 30 209 157 58 177 18 178 210 69 21 209 218 71 22 120 24 148 52 84 100 163 93 23 5 185 65 66 105 219 78 125 77 227 80 81 129 25 154 59 90 155 170 65 171 12 193 113 192 33 87 228 134 86 237 90 41 139 26 33 161 17 122 177 72 176 178 200 81 121 41 96 143 49 237 99 245 148 246 27 166 39 71 167 78 183 43 113 208 89 49 209 247 246 105 58 255 109 254 158 28 173 77 45 172 85 50 138 190 216 96 97 215 256 114 67 161 265 118 167 266 29 115 179 51 131 92 197 127 57 224 223 104 144 264 76 265 123 274 128 275 127 30 185 89 121 137 46 99 204 205 232 231 72 112 274 132 180 85 284 283 137 186

In another example, if the maximum number of sequences per each group is predetermined to 3, the grouping can be performed as shown in the following tables 25 and 26. The tables 25 and 26 are also the case when the base sequences are selected by actual cross correlation calculation.

TABLE 25 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 1 1 25 2 20 2 3 25 57 4 75 60 79 4 2 2 3 4 40 33 65 28 7 71 96 64 45 75 3 3 14 6 7 21 53 9 46 10 37 11 39 86 4 4 6 47 9 66 56 41 14 85 78 15 71 14 5 5 39 39 47 54 44 50 71 44 60 56 75 103 6 6 9 31 61 14 17 84 21 92 85 97 50 67 7 7 42 33 16 28 20 87 24 51 60 82 63 26 8 8 12 30 42 54 23 5 28 99 49 67 86 1 9 9 45 17 68 21 48 85 31 74 58 61 89 78 10 10 15 19 23 5 73 29 106 70 34 93 112 36 11 11 1 21 11 25 32 2 38 102 11 40 78 12 12 12 37 23 51 63 79 64 95 77 41 72 44 100 13 13 4 5 6 30 67 37 45 9 18 104 47 85 14 14 21 7 32 22 40 58 102 84 48 51 6 23 15 15 23 58 58 34 43 61 105 16 25 17 111 83 16 16 24 1 13 65 46 28 91 2 82 96 2 30 17 17 26 52 39 49 31 49 23 59 16 62 107 90 18 18 43 54 65 41 22 52 62 98 89 9 66 28 19 19 29 36 8 20 10 25 30 12 87 41 24 70 20 20 46 38 46 60 87 57 69 5 96 73 35 101 21 21 32 40 48 66 16 60 1 37 73 20 1 39 22 22 2 42 3 50 41 78 76 49 33 52 24 35 23 23 35 29 29 17 66 55 79 8 58 46 27 112 24 24 5 26 55 43 69 2 83 56 47 31 12 88 25 25 38 28 10 57 72 27 15 65 86 63 46 16 26 26 8 20 24 17 45 75 63 54 90 95 57 38 27 27 41 22 62 44 33 48 93 22 29 23 98 42 28 28 33 53 64 50 36 80 61 97 70 102 57 74 29 29 44 8 31 38 24 39 100 36 11 49 68 106 30 30 22 55 69 51 86 64 50 103 18 34 109 81 Gr. Idx 3RBs 12RB 15RB 16RB  1 74 51 4 6 95 140 6 102 70  2 9 120 44 101 71 131 76 12 108  3 83 13 14 17 107 77 18 114 19  4 18 122 87 23 83 113 25 152 120  5 92 23 115 29 118 148 30 158 174  6 27 96 131 35 154 124 37 132 101  7 101 124 32 40 130 160 43 139 107  8 36 105 8 46 136 106 49 113 145  9 133 110 41 52 141 171 151 103 56 10 45 114 91 58 147 57 62 157 189 11 119 3 50 64 153 4 68 67 163 12 54 100 123 69 159 129 74 169 10 13 12 58 128 75 165 135 80 176 81 14 63 132 7 81 21 170 86 150 182 15 67 137 21 86 27 176 188 93 29 16 2 118 71 93 152 3 3 98 162 17 7 76 77 158 98 9 105 41 9 18 11 127 81 104 14 44 111 47 15 19 85 39 16 20 50 110 117 22 181 20 136 20 89 115 26 175 28 123 124 21 94 48 25 121 32 122 129 34 2 22 6 64 52 127 38 8 135 136 59 23 103 34 131 133 73 132 142 78 46 24 38 15 73 139 49 19 148 52 84 25 112 66 43 144 25 55 154 59 90 26 47 116 24 150 61 31 33 161 17 27 121 75 52 156 96 155 166 39 71 28 56 79 126 162 72 102 173 77 45 29 130 95 19 78 48 108 115 179 51 30 65 135 134 173 54 84 185 89 121

TABLE 26 Gr. Idx 3RBs 18RB 20RB 24RB 25RB 1 112 7 6 8 7 167 9 151 150 9 10 156 2 119 14 84 15 135 95 19 207 18 19 165 18 3 20 126 91 23 143 103 28 27 169 28 175 126 4 133 28 168 31 150 190 36 37 178 38 184 135 5 34 175 139 39 38 158 140 45 234 194 48 145 6 41 146 40 46 126 47 55 196 149 56 203 252 7 48 153 118 54 174 173 64 205 158 66 213 212 8 54 195 139 62 181 221 73 214 262 76 222 75 9 61 202 62 69 189 70 82 223 81 85 231 183 10 68 174 209 77 197 157 91 280 92 95 241 192 11 75 74 76 85 204 5 242 195 6 104 250 251 12 187 152 81 92 13 172 109 110 204 113 260 211 13 194 36 141 220 180 101 119 213 260 123 269 25 14 95 201 25 108 107 109 128 33 270 132 230 133 15 102 208 32 116 36 235 137 136 138 288 142 44 16 109 3 179 123 203 4 146 147 4 5 151 249 17 116 10 186 131 132 130 155 13 249 161 63 160 18 17 175 70 19 59 138 164 70 23 170 24 268 19 24 59 130 27 147 146 174 173 32 180 33 179 20 136 31 137 35 154 234 41 183 277 189 43 42 21 143 37 2 162 42 82 192 50 3 198 52 101 22 150 9 149 170 169 50 201 60 202 208 62 110 23 16 30 209 58 177 18 210 69 21 218 71 22 24 163 93 23 185 65 66 219 78 125 227 80 81 25 170 65 171 193 113 192 87 228 134 237 90 41 26 177 72 176 200 81 121 96 143 49 99 245 148 27 78 183 43 208 89 49 247 246 105 255 109 254 28 85 50 138 216 96 97 256 114 67 265 118 167 29 92 197 127 224 223 104 264 76 265 274 128 275 30 46 99 204 232 231 72 274 132 180 284 283 137

In another example, if the maximum number of sequences per each group is predetermined to 2, the grouping can be performed as shown in the following table 27. The table 27 is also the case when the base sequences are selected by actual cross correlation calculation.

TABLE 27 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 15RB 1 1 25 2 20 2 3 25 57 4 60 79 74 51 6 95 2 2 3 4 40 33 65 28 7 71 64 45 9 120 101 71 3 3 14 6 7 21 53 9 46 10 11 39 83 13 17 107 4 4 6 47 9 66 56 41 14 85 15 71 18 122 23 83 5 5 39 39 47 54 44 50 71 44 56 75 92 23 29 118 6 6 9 31 61 14 17 84 21 92 97 50 27 96 35 154 7 7 42 33 16 28 20 87 24 51 82 63 101 124 40 130 8 8 12 30 42 54 23 5 28 99 67 86 36 105 46 136 9 9 45 17 68 21 48 85 31 74 61 89 133 110 52 141 10 10 15 19 23 5 73 29 106 70 93 112 45 114 58 147 11 11 1 21 11 25 32 2 38 102 40 78 119 3 64 153 12 12 37 23 51 63 79 64 95 77 72 44 54 100 69 159 13 13 4 5 6 30 67 37 45 9 104 47 12 58 75 165 14 14 21 7 32 22 40 58 102 84 51 6 63 132 81 21 15 15 23 58 58 34 43 61 105 16 17 111 67 137 86 27 16 16 24 1 13 65 46 28 91 2 96 2 2 118 93 152 17 17 26 52 39 49 31 49 23 59 62 107 7 76 158 98 18 18 43 54 65 41 22 52 62 98 9 66 11 127 104 14 19 19 29 36 8 20 10 25 30 12 41 24 85 39 20 50 20 20 46 38 46 60 87 57 69 5 73 35 136 20 115 26 21 21 32 40 48 66 16 60 1 37 20 1 94 48 121 32 22 22 2 42 3 50 41 78 76 49 52 24 6 64 127 38 23 23 35 29 29 17 66 55 79 8 46 27 103 34 133 73 24 24 5 26 55 43 69 2 83 56 31 12 38 15 139 49 25 25 38 28 10 57 72 27 15 65 63 46 112 66 144 25 26 26 8 20 24 17 45 75 63 54 95 57 47 116 150 61 27 27 41 22 62 44 33 48 93 22 23 98 121 75 156 96 28 28 33 53 64 50 36 80 61 97 102 57 56 79 162 72 29 29 44 8 31 38 24 39 100 36 49 68 130 95 78 48 30 30 22 55 69 51 86 64 50 103 34 109 65 135 173 54 Gr. Idx 3RBs 16RB 18RB 20RB 24RB 25RBs  1 6 102 112 7 8 7 9 151 9 10  2 76 12 119 14 15 135 19 207 19 165  3 18 114 20 126 23 143 28 27 28 175  4 25 152 133 28 31 150 36 37 38 184  5 30 158 34 175 39 38 140 45 194 48  6 37 132 41 146 46 126 55 196 56 203  7 43 139 48 153 54 174 64 205 66 213  8 49 113 54 195 62 181 73 214 76 222  9 151 103 61 202 69 189 82 223 85 231 10 62 157 68 174 77 197 91 280 95 241 11 68 67 75 74 85 204 242 195 104 250 12 74 169 187 152 92 13 109 110 113 260 13 80 176 194 36 220 180 119 213 123 269 14 86 150 95 201 108 107 128 33 132 230 15 188 93 102 208 116 36 137 136 288 142 16 3 98 109 3 123 203 146 147 5 151 17 105 41 116 10 131 132 155 13 161 63 18 111 47 17 175 19 59 164 70 170 24 19 117 22 24 59 27 147 174 173 180 33 20 28 123 136 31 35 154 41 183 189 43 21 129 34 143 37 162 42 192 50 198 52 22 135 136 150 9 170 169 201 60 208 62 23 142 78 16 30 58 177 210 69 218 71 24 148 52 163 93 185 65 219 78 227 80 25 154 59 170 65 193 113 87 228 237 90 26 33 161 177 72 200 81 96 143 99 245 27 166 39 78 183 208 89 247 246 255 109 28 173 77 85 50 216 96 256 114 265 118 29 115 179 92 197 224 223 264 76 274 128 30 185 89 46 99 232 231 274 132 284 283

In another example, if the maximum number of sequences per each group is predetermined to 1, the grouping can be performed as shown in the following table 28. The table 28 is also the case when the base sequences are selected by actual cross correlation calculation.

TABLE 28 Gr. Idx 3RBs 3RB 4RB 5RB 6RB 8RB 9RB 10RB 12RB 15RB 16RB 18RB 20RB 24RB 25RBs 1 1 25 2 20 3 57 60 74 6 6 112 8 9 9 2 2 3 4 40 65 7 64 9 101 76 119 15 19 19 3 3 14 6 7 53 46 11 83 17 18 20 23 28 28 4 4 6 47 9 56 14 15 18 23 25 133 31 36 38 5 5 39 39 47 44 71 56 92 29 30 34 39 140 194 6 6 9 31 61 17 21 97 27 35 37 41 46 55 56 7 7 42 33 16 20 24 82 101 40 43 48 54 64 66 8 8 12 30 42 23 28 67 36 46 49 54 62 73 76 9 9 45 17 68 48 31 61 133 52 151 61 69 82 85 10 10 15 19 23 73 106 93 45 58 62 68 77 91 95 11 11 1 21 11 32 38 40 119 64 68 75 85 242 104 12 12 37 23 51 79 95 72 54 69 74 187 92 109 113 13 13 4 5 6 67 45 104 12 75 80 194 220 119 123 14 14 21 7 32 40 102 51 63 81 86 95 108 128 132 15 15 23 58 58 43 105 17 67 86 188 102 116 137 288 16 16 24 1 13 46 91 96 2 93 3 109 123 146 5 17 17 26 52 39 31 23 62 7 158 105 116 131 155 161 18 18 43 54 65 22 62 9 11 104 111 17 19 164 170 19 19 29 36 8 10 30 41 85 20 117 24 27 174 180 20 20 46 38 46 87 69 73 136 115 28 136 35 41 189 21 21 32 40 48 16 1 20 94 121 129 143 162 192 198 22 22 2 42 3 41 76 52 6 127 135 150 170 201 208 23 23 35 29 29 66 79 46 103 133 142 16 58 210 218 24 24 5 26 55 69 83 31 38 139 148 163 185 219 227 25 25 38 28 10 72 15 63 112 144 154 170 193 87 237 26 26 8 20 24 45 63 95 47 150 33 177 200 96 99 27 27 41 22 62 33 93 23 121 156 166 78 208 247 255 28 28 33 53 64 36 61 102 56 162 173 85 216 256 265 29 29 44 8 31 24 100 49 130 78 115 92 224 264 274 30 30 22 55 69 86 50 34 65 173 185 46 232 274 284

For the above cases, the tables can be reorganized according to the allocated number of sequence per each group and each length.

For another example of this invention, the above tables can be extended to 100 RB length, and following tables show this example. In this example, the maximum number of the root index number (v) for 5 RB length or less is set to 1, and maximum number of the root index number (v) for the length longer than 5 RB is set to 2.

TABLE 29 RB 3 4 5 6 8 9 10 12 15 Nzc 31 47 59 71 89 107 113 139 179 Max 1 1 1 2 2 2 2 2 2 root per Gr. RB Idx v 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 2 2 2 3 3 2 3 4 4 3 4 5 6 5 1 1 3 4 5 4 6 5 7 6 7 8 9 8 12 11 2 2 5 6 7 6 9 8 10 11 11 10 13 14 17 18 3 3 6 8 9 10 11 12 14 13 15 14 18 17 23 24 4 4 8 10 11 12 14 15 17 18 18 19 22 23 29 28 5 5 9 11 14 13 17 18 21 20 22 21 27 26 35 34 6 6 11 13 16 17 20 21 24 25 26 25 31 32 40 41 7 7 12 15 18 19 23 22 28 27 29 30 36 35 46 47 8 8 14 17 21 20 26 25 31 32 33 32 40 41 52 51 9 9 15 19 23 22 29 28 35 34 36 37 45 44 58 57 10 10 17 21 25 26 32 31 38 37 40 41 49 50 64 63 11 11 18 23 27 28 34 35 41 42 44 43 54 53 69 70 12 12 20 25 30 29 37 38 45 44 47 48 58 59 75 76 13 13 21 27 32 33 40 41 48 49 51 52 63 62 81 80 14 14 23 29 34 35 43 44 52 51 55 54 67 68 87 86 15 15 24 30 37 36 46 45 55 56 58 59 72 71 92 93 16 16 26 32 39 38 49 48 59 58 62 61 76 77 98 99 17 17 27 34 41 42 52 51 62 63 66 65 81 80 104 103 18 18 29 36 44 43 55 54 66 65 69 70 85 86 110 109 19 19 30 38 46 45 57 58 69 70 73 72 90 89 115 116 20 20 32 40 48 49 60 61 72 73 77 76 94 95 121 122 21 21 33 42 50 51 63 64 76 75 80 81 99 98 127 128 22 22 35 44 53 52 66 67 79 80 84 83 103 104 133 132 23 23 36 46 55 54 69 68 83 82 87 88 108 107 139 138 24 24 38 48 57 58 72 71 86 87 91 92 112 113 144 145 25 25 39 49 60 59 75 74 90 89 95 94 117 116 150 151 26 26 41 51 62 61 78 77 93 94 98 99 121 122 156 155 27 27 42 53 64 65 80 81 97 96 102 103 126 125 162 161 28 28 44 55 66 67 83 84 100 101 106 105 130 131 167 168 29 29 45 57 69 68 86 87 104 103 109 110 135 134 173 174

TABLE 30 RB 16 18 20 24 25 27 30 32 Nzc 191 211 239 283 293 317 359 383 Max 2 2 2 2 2 2 2 2 root per Gr. RB Idx v 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 6 7 7 6 8 7 9 10 9 10 10 11 12 11 12 13 1 12 13 14 13 15 16 18 19 19 18 20 21 23 24 25 24 2 18 19 20 21 23 24 27 28 28 29 31 30 35 34 37 38 3 25 24 27 28 31 30 37 36 38 37 41 40 46 47 49 50 4 31 30 34 35 39 38 46 45 47 48 51 52 58 57 62 61 5 37 36 41 40 46 47 55 54 57 56 61 62 69 70 74 75 6 43 44 48 47 54 53 64 63 66 67 72 71 81 82 86 87 7 49 50 54 55 62 61 73 74 76 75 82 81 93 92 99 98 8 55 56 61 62 69 70 82 83 85 86 92 93 104 105 111 112 9 62 61 68 69 77 78 91 92 95 94 102 103 116 115 124 123 10 68 67 75 74 85 84 100 101 104 103 112 113 127 128 136 135 11 74 73 82 81 93 92 110 109 113 114 123 122 139 138 148 149 12 80 81 88 89 100 101 119 118 123 122 133 132 151 150 161 160 13 86 87 95 96 108 107 128 127 132 133 143 144 162 163 173 172 14 92 93 102 103 116 115 137 136 142 141 153 154 174 173 185 186 15 99 98 109 108 123 124 146 147 151 152 164 163 185 186 198 197 16 105 104 116 115 131 132 155 156 161 160 174 173 197 196 210 211 17 111 110 123 122 139 138 164 165 170 171 184 185 208 209 222 223 18 117 118 129 130 146 147 173 174 180 179 194 195 220 221 235 234 19 123 124 136 137 154 155 183 182 189 190 205 204 232 231 247 248 20 129 130 143 142 162 161 192 191 198 199 215 214 243 244 259 260 21 136 135 150 149 170 169 201 200 208 207 225 224 255 254 272 271 22 142 141 157 156 177 178 210 209 217 218 235 236 266 267 284 285 23 148 147 163 164 185 186 219 220 227 226 245 246 278 277 297 296 24 154 155 170 171 193 192 228 229 236 237 256 255 290 289 309 308 25 160 161 177 176 200 201 237 238 246 245 266 265 301 302 321 322 26 166 167 184 183 208 209 246 247 255 256 276 277 313 312 334 333 27 173 172 191 190 216 215 256 255 265 264 286 287 324 325 346 345 28 179 178 197 198 224 223 265 264 274 275 297 296 336 335 358 359 29 185 184 204 205 231 232 274 273 284 283 307 306 347 348 371 370

TABLE 31 1 RB 36 40 45 48 50 54 60 64 2 Nzc 431 479 523 571 599 647 719 761 Max 2 2 2 2 2 2 2 2 root per Gr. RB Idx v 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 14 13 15 16 17 16 18 19 19 20 21 20 23 24 25 24 1 28 27 31 30 34 33 37 36 39 38 42 41 46 47 49 50 2 42 41 46 47 51 50 55 56 58 57 63 62 70 69 74 73 3 56 55 62 61 67 68 74 73 77 78 83 84 93 92 98 99 4 70 69 77 78 84 85 92 93 97 96 104 105 116 115 123 122 5 83 84 93 92 101 102 111 110 116 115 125 126 139 140 147 148 6 97 98 108 109 118 119 129 128 135 136 146 147 162 163 172 171 7 111 112 124 123 135 134 147 148 155 154 167 166 186 185 196 197 8 125 126 139 140 152 151 166 165 174 173 188 187 209 208 221 220 9 139 140 155 154 169 168 184 185 193 194 209 208 232 231 245 246 10 153 152 170 169 186 185 203 202 213 212 230 229 255 256 270 271 11 167 166 185 186 202 203 221 222 232 231 250 251 278 279 295 294 12 181 180 201 200 219 220 239 240 251 252 271 272 302 301 319 320 13 195 194 216 217 236 237 258 257 271 270 292 293 325 324 344 343 14 209 208 232 231 253 254 276 277 290 289 313 314 348 347 368 369 15 222 223 247 248 270 269 295 294 309 310 334 333 371 372 393 392 16 236 237 263 262 287 286 313 314 328 329 355 354 394 395 417 418 17 250 251 278 279 304 303 332 331 348 347 376 375 417 418 442 441 18 264 265 294 293 321 320 350 349 367 368 397 396 441 440 466 467 19 278 279 309 310 337 338 368 369 386 387 417 418 464 463 491 490 20 292 291 324 325 354 355 387 386 406 405 438 439 487 488 516 515 21 306 305 340 339 371 372 405 406 425 426 459 460 510 511 540 541 22 320 319 355 356 388 389 424 423 444 445 480 481 533 534 565 564 23 334 333 371 370 405 404 442 443 464 463 501 500 557 556 589 590 24 348 347 386 387 422 421 460 461 483 484 522 521 580 579 614 613 25 361 362 402 401 439 438 479 478 502 503 543 542 603 604 638 639 26 375 376 417 418 456 455 497 498 522 521 564 563 626 627 663 662 27 389 390 433 432 472 473 516 515 541 542 584 585 649 650 687 688 28 403 404 448 449 489 490 534 535 560 561 605 606 673 672 712 711 29 417 418 464 463 506 507 553 552 580 579 626 627 696 695 736 737

TABLE 32 1 RB 72 75 80 81 90 96 100 2 Nzc 863 887 953 971 1069 1151 1193 Max 2 2 2 2 2 2 2 root per Gr. RB Idx v 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 28 27 29 28 31 30 31 32 34 35 37 38 38 39 1 56 55 57 58 61 62 63 62 69 68 74 75 77 76 2 84 83 86 85 92 93 94 93 103 104 111 112 115 116 3 111 112 114 115 123 122 125 126 138 137 149 148 154 153 4 139 140 143 144 154 153 157 156 172 173 186 185 192 193 5 167 168 172 171 184 185 188 187 207 206 223 222 231 230 6 195 194 200 201 215 216 219 220 241 242 260 259 269 270 7 223 222 229 228 246 245 251 250 276 275 297 298 308 307 8 251 250 258 257 277 276 282 281 310 311 334 335 346 347 9 278 279 286 287 307 308 313 314 345 344 371 372 385 384 10 306 307 315 314 338 339 345 344 379 380 408 409 423 424 11 334 335 343 344 369 368 376 375 414 413 446 445 462 461 12 362 361 372 371 400 399 407 408 448 449 483 482 500 501 13 390 389 401 400 430 431 439 438 483 482 520 519 539 538 14 418 417 429 430 461 462 470 469 517 518 557 556 577 578 15 445 446 458 457 492 491 501 502 552 551 594 595 616 615 16 473 474 486 487 523 522 532 533 586 587 631 632 654 655 17 501 502 515 516 553 554 564 563 621 620 668 669 693 692 18 529 528 544 543 584 585 595 596 655 656 705 706 731 732 19 557 556 572 573 615 614 626 627 690 689 743 742 770 769 20 585 584 601 600 646 645 658 657 724 725 780 779 808 809 21 612 613 629 630 676 677 689 690 759 758 817 816 847 846 22 640 641 658 659 707 708 720 721 793 794 854 853 885 886 23 668 669 687 686 738 737 752 751 828 827 891 892 924 923 24 696 695 715 716 769 768 783 784 862 863 928 929 962 963 25 724 723 744 743 799 800 814 815 897 896 965 966 1001 1000 26 752 751 773 772 830 831 846 845 931 932 1002 1003 1039 1040 27 779 780 801 802 861 860 877 878 966 965 1040 1039 1078 1077 28 807 808 830 829 892 891 908 909 1000 1001 1077 1076 1116 1117 29 835 836 858 859 922 923 940 939 1035 1034 1114 1113 1155 1154

Based on these concepts, the present invention provides a method for generating reference signal sequence using ZC sequence as follows.

To generate reference signal sequence, one embodiment of the present invention defines a specific base sequence for allying cyclic shift. In this embodiment, the base sequence is defined using ZC sequence with certain root index (hereinafter “q”). And, the specific base sequence is selected from the base sequence groups, and each of the base sequence group contains base sequences having a high cross correlation relation as stated above. So, if one wants to select the specific base sequence with index of “q”, the “q” should be selected considering the group index (hereinafter “u”) and the base sequence number index within each group (hereinafter “v”). That is, “q” should be a function of “u” and “v”.

And, after the specific base sequence with root index “q” is selected, then the cyclic shift corresponding to various cyclic shift values can be applied to the selected base sequence.

If the relation between the “q”, “u” and “v” is more specifically considered, “q” can be acquired by the following equations. The following equations 17 and 18 are for selecting the index “q” to meet the condition that the term (s₁/N₁−s₂/N₂) becomes close to zero.

$\begin{matrix} {\mspace{79mu}{{q = {{{round}(y)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}\;{({{{round}\;{(y)}} - y})}} + v}}}}\mspace{79mu}{where}\mspace{79mu}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS}}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack \\ {{q = {{{floor}\;\left( {y + 0.5} \right)} + {{{floor}\left( \frac{v + 1}{2} \right)} \cdot \left( {- 1} \right)^{{{floor}\;{({{{floor}\;{({y + 0.5})}} - y})}} + v}}}}\mspace{79mu}{where}\mspace{79mu}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference},\;{zc}}^{RS}}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack \end{matrix}$

Here, N_(zc) ^(RS) is the target ZC sequence generation length used in generating the q-th root ZC sequence, and N_(zc) ^(RS) is given by the largest prime number which is less than the corresponding reference signal sequence size. That is, the base sequence is generated by cyclic extension method.

And, N_(reference,zc) ^(RS) is the length given by the largest prime number which is less than the reference sequence size, for example, 3 RB length. If the grouping is based on the 3 RB length, then N_(reference,zc) ^(RS) is 31. The “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z.

And, according to another embodiment of this invention, if the ZC sequence is generated based on the truncation method, then N_(zc) ^(RS) can be given by the smallest prime number which is greater than the corresponding reference signal sequence size. And, in this case, N_(reference,zc) ^(RS) can be the length given by the smallest prime number which is greater than the reference sequence size, for example, 3 RB length. If the grouping is based on the 3 RB length, then N_(reference,zc) ^(RS) can be 37.

And, according to equations 17 and 18, “m”-th element of the “q”-th ZC sequence (x_(q)(m)) can be expressed as follows.

$\begin{matrix} {{{x_{q}(m)} = e^{{- j}\frac{\pi\;{{qm}{({m + 1})}}}{N_{ZC}^{RS}}}},\mspace{11mu}{0 \leq m \leq {N_{ZC}^{RS} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack \end{matrix}$

Because “round (y)” and “floor (y+0.5)” are actually equivalent, the equations 17 and 18 have the same meaning. In the equations 17 and 18, the term (−1)^(floor(round(y)−y)) means that if “y” has 0.5 or greater value in its decimal place, (−1)^(floor(round(y)−y)) can be calculated as “1”, and if “y” has the value less than 0.5 in its decimal place, (−1)^(floor(round(y)−y)) can be calculated as “−1”. So, (−1)^(floor(round(y)−y)) can be replaced with (−1)^(floor(y-round(y))+1) or any other equivalent terms having the same meaning.

In the above examples, when the grouping is performed for the length greater than the 3 RB length based on the 3 RB length, and when the ZC sequence is generated based on the cyclic extension method, N_(reference,zc) ^(RS) can be 31. Also, when the ZC sequence is generated based on the truncation method, N_(reference,zc) ^(RS) can be 37. And, when the grouping is performed for the length greater than the 4 RB length based on the 4 RB length, and when the ZC sequence is generated based on the cyclic extension method, N_(reference,zc) ^(RS) can be 47. Also, when the ZC sequence is generated based on the truncation method, N_(reference,zc) ^(RS) can be 49. And, this can be easily employed to other length based grouping.

Above mentioned tables can be acquired by the equations 17 and 18. The following examples are part of selecting root index according to the equations 17 and 18.

First, if the N_(reference,zc)=31, the method for selecting first group (“u”=0) when 1) Nzc=47, 2) Nzc=71 3)Nzc=211 is as follows. In the following examples, the equation 18 is used.

${{\left. 1 \right)\mspace{14mu} N_{{reference},\;{zc}}} = 31},\mspace{11mu}{N_{zc}^{RS} = 47},\mspace{14mu}{u = 0},\;{{v = 0};\mspace{11mu}{y = {47/31}}},{q = {{\left\lfloor {\frac{47}{31} + 0.5} \right\rfloor + {\left\lfloor \frac{0 + 1}{2} \right\rfloor \cdot \left( {- 1} \right)^{{\lfloor{{\lfloor{\frac{47}{31} + 0.5}\rfloor} - \frac{47}{31}}\rfloor} + 0}}} = 2}}$

So, for 4 RB length, the first base sequence number (v=0) in the first group (u=0) is 2 (q=2).

${{\left. 2 \right)\mspace{14mu} N_{{reference}\;,\;{zc}}} = 31},\mspace{11mu}{N_{zc}^{RS} = 71},\mspace{11mu}{u = 0},\mspace{11mu}{{v = 0};\mspace{11mu}{y = {71/31}}},{q = {{\left\lfloor {\frac{71}{31} + 0.5} \right\rfloor + {\left\lfloor \frac{0 + 1}{2} \right\rfloor \cdot \left( {- 1} \right)^{{\lfloor{{\lfloor{\frac{71}{31} + 0.5}\rfloor} - \frac{71}{31}}\rfloor} + 0}}} = 2}}$

So, for 6 RB length, the first base sequence number (v=0) in the first group (u=0) is 2 (q=2).

${{\left. 3 \right)\mspace{14mu} N_{{reference}\;,\;{zc}}} = 31},\mspace{11mu}{N_{zc}^{RS} = 211},\mspace{11mu}{u = 0},\mspace{11mu}{{v = 0};\mspace{11mu}{y = {211/31}}},{q = {{\left\lfloor {\frac{211}{31} + 0.5} \right\rfloor + {\left\lfloor \frac{0 + 1}{2} \right\rfloor \cdot \left( {- 1} \right)^{{\lfloor{{\lfloor{\frac{211}{31} + 0.5}\rfloor} - \frac{211}{31}}\rfloor} + 0}}} = 7}}$

So, for 18 RB length, the first base sequence number (v=0) in the first group (u=0) is 7 (q=7).

For the above cases, the selected root indexes (q) correspond to the data in tables 6˜8 which are generated based on 3 RB length.

In another example, if the N_(reference,zc)=47 (based on 4 RB length), the method for selecting the second group (“u”=1) when 1) Nzc=59, 2) Nzc=107 3)Nzc=139 is as follows. In the following examples, the equation 18 is used.

${{\left. 1 \right)\mspace{14mu} N_{{reference}\;,\;{zc}}} = 47},\mspace{11mu}{N_{zc}^{RS} = 59},\mspace{11mu}{u = 1},\mspace{11mu}{{v = 0};\mspace{11mu}{y = {{59/47}*2}}},{q = {{\left\lfloor {\frac{59 \cdot}{47} + 0.5} \right\rfloor + {\left\lfloor \frac{0 + 1}{2} \right\rfloor \cdot \left( {- 1} \right)^{{\lfloor{{\lfloor{\frac{59 \cdot 2}{47} + 0.5}\rfloor} - \frac{59.2}{47}}\rfloor} + 0}}} = 3}}$

So, for 5 RB length, the first base sequence number (v=0) in the second group (u=1) is 3 (q=3).

${{\left. 2 \right)\mspace{20mu} N_{{reference},\mspace{11mu}{zc}}} = 47},\mspace{11mu}{N_{zc}^{RS} = 107},\mspace{11mu}{u = 1},\mspace{11mu}{{v = 0};\mspace{11mu}{y = {{107/47}*2}}},{q = {{\left\lfloor {\frac{107 \cdot 2}{47} + 0.5} \right\rfloor + {\left\lfloor \frac{0 + 1}{2} \right\rfloor \cdot \left( {- 1} \right)^{{\lfloor{{\lfloor{\frac{107 \cdot 2}{47} + 0.5}\rfloor} - \frac{107 \cdot 2}{47}}\rfloor} + 0}}} = 5}}$

So, for 9 RB length, the first base sequence number (v=0) in the second group (u=1) is 5 (q=5).

${{\left. 3 \right)\mspace{14mu} N_{{reference}\;,\;{zc}}} = 47},\mspace{11mu}{N_{zc}^{RS} = 139},\mspace{11mu}{u = 1},\mspace{11mu}{{v = 0};\;{y = {{139/47}*2}}},{q = {{\left\lfloor {\frac{139 \cdot 2}{47} + 0.5} \right\rfloor + {\left\lfloor \frac{0 + 1}{2} \right\rfloor \cdot \left( {- 1} \right)^{{\lfloor{{\lfloor{\frac{139 \cdot 2}{47} + 0.5}\rfloor} - \frac{139 \cdot 2}{47}}\rfloor} + 0}}} = 6}}$

So, for 12 RB length, the first base sequence number (v=0) in the second group (u=1) is 6 (q=6).

In another embodiment of the present invention, the equations 17 and 18 can be replaced as follows.

$\begin{matrix} {\mspace{79mu}{{q = {{{round}(y)} + {{floor}\;{\left( \frac{v + 1}{2} \right) \cdot \left( {- 1} \right)^{{{floor}\;{({{{round}\;{(y)}} - y})}} + v}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS} - 1}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\;\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack \\ {{q = {{{floor}\;\left( {y + 0.5} \right)} + {{floor}\;{\left( \frac{v + 1}{2} \right) \cdot \left( {- 1} \right)^{{{floor}{({{{floor}\;{({y + 0.5})}} - y})}} + v}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS} - 1}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack \end{matrix}$

Because “round (y)” and “floor (y+0.5)” are actually equivalent, the equations 20 and 21 have the same meaning.

In another embodiment of the present invention, the equations 17 and 18 can be replaced as follows.

$\begin{matrix} {\mspace{79mu}{{q = {{{round}\mspace{11mu}(y)} + {{floor}\;{\left( \frac{v + 1}{2} \right) \cdot \left( {- 1} \right)^{{{floor}({{{round}\;{(y)}}\; - y}\;)} + v}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = {{round}\;{\left( \frac{N_{zc}^{RS}}{N_{{reference}\;,{zc}}^{RS}} \right) \cdot \left( {u + 1} \right)}}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack \\ {{q = {{{floor}\mspace{11mu}\left( {y + 0.5} \right)} + {{floor}\;{\left( \frac{v + 1}{2} \right) \cdot \left( {- 1} \right)^{{{floor}\;{({{{floor}\;{({y + 0.5})}} - y})}} + v}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = {{floor}\;{\left( {\frac{N_{zc}^{RS}}{N_{{reference}\;,\;{zc}}^{RS}} + 0.5} \right) \cdot \left( {u + 1} \right)}}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\mspace{11mu}\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack \end{matrix}$

These equations correspond to various grouping method explained with regard to the above mentioned tables.

If the maximum number of sequences, which can be grouped in one group, are predetermined to 2, the equations 17-18, 20-21 and 22-23 can be simplified as follows, respectively.

$\begin{matrix} {{q = {{{round}\;(y)} + {v \cdot \left( {- 1} \right)^{{floor}\;{({2y})}}}}}{where}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS}}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack \\ {{q = {{{floor}\;\left( {y + 0.5} \right)} + {v \cdot \left( {- 1} \right)^{{floor}\;{({2y})}}}}}{where}{{y = \frac{N_{zc}^{RS} \cdot \left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS}}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack \\ {{q = {{{round}\;(y)} + {v \cdot \left( {- 1} \right)^{{floor}\;{({2y})}}}}}{where}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS} - 1}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack \\ {{q = {{{floor}\;\left( {y + 0.5} \right)} + {v \cdot \left( {- 1} \right)^{{floor}\;{({2y})}}}}}{where}{{y = \frac{\left( {N_{zc}^{RS} - 1} \right) \cdot \left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS} - 1}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack \\ {{q = {{{round}\;(y)} + {v \cdot \left( {- 1} \right)^{{floor}\;{({2y})}}}}}{where}{{y = {{round}\;{\left( \frac{N_{zc}^{RS}}{N_{{reference}\;,\;{zc}}^{RS}} \right) \cdot \left( {u + 1} \right)}}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack \\ {{q = {{{floor}\;\left( {y + 0.5} \right)} + {v \cdot (1)^{{floor}\;{({2y})}}}}}{where}{{y = {{floor}\;{\left( {\frac{N_{zc}^{RS}}{N_{{reference}\;,\;{zc}}^{RS}} + 0.5} \right) \cdot \left( {u + 1} \right)}}},{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},{v \in \left\{ {0,1} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack \end{matrix}$

The equations 17-18, 20-21 and 22-23 are for selecting ZC root index to meet the condition that the term (s₁/N₁−s₂/N₂) become close to zero. And, the equations 24-29 are for selecting root index ZC root index when the maximum number of sequences per groups of each length is limited to 2.

But if we make these equations to be more generalized such that the term (s₁/N₁−s₂/N₂) become close to a specific value (T), the following equations can be acquired. In this case, the value “T” can be 0, ½, −½, ⅓, −⅓. But value “T” can have other value.

In the following equations, the equations 30 and 31 are for selecting ZC root index when the maximum number of sequence per group of each length can have the maximum value. And, the equations 32 and 33 are for selecting ZC root index when the maximum number of sequence per group of each length is limited to 2.

$\begin{matrix} {\mspace{79mu}{{q = {{{round}\;(y)} + {{floor}\;{\left( \frac{v + 1}{2} \right) \cdot \left( {- 1} \right)^{{{floor}\;{({{{round}\;{(y)}} - y})}} + v}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = {N_{zc}^{RS} \cdot \left( {T + \frac{\left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS}}} \right)}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\;\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack \\ {{q = {{{floor}\;\left( {y + 0.5} \right)} + {{floor}\;{\left( \frac{v + 1}{2} \right) \cdot \left( {- 1} \right)^{{{floor}{({{{floor}\;{({y + 0.5})}} - y})}} + v}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = {N_{zc}^{RS} \cdot \left( {T + \frac{\left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS}}} \right)}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1,\ldots\mspace{14mu},{{{floor}\;\left( {N_{ZC}^{RS}/30} \right)} - 1}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack \\ {\mspace{79mu}{{q = {{{round}\;(y)} + {v \cdot \left( {- 1} \right)^{{floor}\;{({2y})}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = {N_{zc}^{RS} \cdot \left( {T + \frac{\left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS}}} \right)}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 32} \right\rbrack \\ {\mspace{79mu}{{q = {{{floor}\;\left( {y + 0.5} \right)} + {v \cdot (1)^{{floor}\;{({2y})}}}}}\mspace{79mu}{where}\mspace{79mu}{{y = {N_{zc}^{RS} \cdot \left( {T + \frac{\left( {u + 1} \right)}{N_{{reference}\;,\;{zc}}^{RS}}} \right)}},\mspace{79mu}{u \in \left\{ {0,1,\ldots\mspace{14mu},29} \right\}},\mspace{79mu}{v \in \left\{ {0,1} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack \end{matrix}$

It will be apparent to those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit and essential characteristics of the invention. Thus, the above embodiments are to be considered in all respects as illustrative and not restrictive. The scope of the invention should be determined by reasonable interpretation of the appended claims and all change which comes within the equivalent scope of the invention are included in the scope of the invention.

According to the embodiments of the present invention, inter cell interference caused by using variable length sequences can be minimized. And, if each grouped base sequence is allocated to specific cell or Node B, UE(s) can use variable length sequence as reference signal.

These methods are appropriate to be employed in 3GPP LTE (3^(rd) Generation Partnership Project Long Term Evolution) system. But, those skilled in the art can easily understand that these methods can be employed to any wireless communication system using various length sequences as a reference signal sequences.

Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims. 

What is claimed is:
 1. A method for a base station to receive a reference signal from a user equipment in a wireless communication system, the method comprising: receiving the reference signal from the user equipment; and processing the received reference signal, wherein the reference signal is defined based on a Zadoff Chu sequence having a length ‘N_(zc) ^(RS)’ and a root index ‘q’, the root index ‘q’ determined based on a group index ‘u’, the length ‘N_(zc) ^(RS)’, and a sequence index ‘v’ for each length ‘N_(zc) ^(RS)’ within a sequence group corresponding to the group index ‘u’, and the group index ‘u’ corresponding to a cell where the user equipment is operating.
 2. The method of claim 1, wherein the determined root index ‘q’ satisfies: q=floor (y+0.5)+v*(−1)^(floor(2y)), wherein: y=N _(zc) ^(RS)*(u+1)/N _(reference), and wherein the ‘N_(reference)’ is a length of a predetermined reference Zadoff-Chu sequence.
 3. The method of claim 1, wherein a number of the sequence index ‘v’ is 1 for the length ‘N_(zc) ^(RS)’ equal to or less than 5 RB (Resource Block) length, and the number of the sequence index ‘v’is 2 for the length ‘N_(zc) ^(RS)’, more than 5 RB length.
 4. The method of claim 3, wherein the ‘N_(reference)’ is predetermined as ‘31’.
 5. A base station for receiving a reference signal from a user equipment in a wireless communication system, the base station comprising: a RF unit for receiving the reference signal from the user equipment; and a processor for processing the reference signal based on that: the reference signal is defined based on a Zadoff Chu sequence having a length ‘N_(zc) ^(RS)’ and a root index ‘q’, the root index ‘q’ determined based on a group index ‘u’, the length ‘N_(zc) ^(RS)’, and a sequence index ‘v’ for each length ‘N_(zc) ^(RS)’ within a sequence group corresponding to the group index ‘u’, the group index ‘u’ corresponding to a cell where the user equipment is operating.
 6. The base station of claim 5, wherein the determined root index ‘q’ satisfies: q=floor (y+0.5)+v*(−1)^(floor(2y)), wherein: y=N _(zc) ^(RS)*(u+1)/N _(reference), and wherein the ‘N_(reference)’ is a length of a predetermined reference Zadoff-Chu sequence.
 7. The base station of claim 6, wherein a number of the sequence index ‘v’ is 1 for the length ‘N_(zc) ^(RS)’ equal to or less than 5 RB (Resource Block) length, and the number of the sequence index ‘v’ is 2 for the length ‘N_(zc) ^(RS’) more than 5 RB length.
 8. The base station of claim 7, wherein the ‘N_(reference)’ is predetermined as ‘31’. 